UNITED STATES
                     SECURITIES AND EXCHANGE COMMISSION
                              Washington, D.C.

                                SCHEDULE 13G


                 UNDER THE SECURITIES EXCHANGE ACT OF 1934
                             (AMENDMENT NO. 2)(1)


                      UNITED STATES STEEL CORPORATION
 -------------------------------------------------------------------------
                              (Name of Issuer)

                                COMMON STOCK
 -------------------------------------------------------------------------
                       (Title of Class of Securities)

                                 912909108
 -------------------------------------------------------------------------
                               (CUSIP Number)

                             December 31, 2004
 -------------------------------------------------------------------------

          (Date of Event Which Requires Filing of this Statement)

          Check the appropriate box to designate the rule pursuant to which
          this Schedule is filed:
               |_| Rule 13d-1(b)
               |X| Rule 13d-1(c)
               |_| Rule 13d-1(d)


          (1) The remainder of this cover page shall be filled out for a
          reporting person's initial filing on this form with respect to
          the subject class of securities, and for any subsequent amendment
          containing information which would alter the disclosures provided
          in a prior cover page.

          The information required in the remainder of this cover page
          shall not be deemed to be "filed" for the purpose of Section 18
          of the Securities Exchange Act of 1934, as amended (the "Act") or
          otherwise subject to the liabilities of that section of the Act
          but shall be subject to all other provisions of the Act (however,
          see the Notes).

                                SCHEDULE 13G

    CUSIP NO. 912909108                                  PAGE 2 OF 11 PAGES


1   NAME OF REPORTING PERSONS.
    I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY).
        APPALOOSA INVESTMENT LIMITED PARTNERSHIP I

2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*    (a)  [ ]
                                                         (b)  [ ]

3   SEC USE ONLY

4   CITIZENSHIP OR PLACE OF ORGANIZATION
        DELAWARE


  NUMBER OF      5  SOLE VOTING POWER

   SHARES               -0-

 BENEFICIALLY    6  SHARED VOTING POWER

OWNED BY EACH           4,168,062

 REPORTING       7  SOLE DISPOSITIVE POWER

PERSON WITH             -0-

                 8  SHARED DISPOSITIVE POWER

                        4,168,062

9   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                4,168,062

10  CHECK IF THE AGGREGATE AMOUNT IN ROW (9)                  [ ]
    EXCLUDES CERTAIN SHARES*

11  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                3.7%

12  TYPE OF REPORTING PERSON*

                PN
                             *SEE INSTRUCTIONS





                                SCHEDULE 13G

    CUSIP NO. 912909108                                  PAGE 3 OF 11 PAGES


1   NAME OF REPORTING PERSONS.
    I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY).
        PALOMINO FUND LTD.

2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*    (a)  [ ]
                                                         (b)  [ ]

3   SEC USE ONLY

4   CITIZENSHIP OR PLACE OF ORGANIZATION
        BRITISH VIRGIN ISLANDS


  NUMBER OF      5  SOLE VOTING POWER

   SHARES               -0-

 BENEFICIALLY    6  SHARED VOTING POWER

OWNED BY EACH           2,539,937

 REPORTING       7  SOLE DISPOSITIVE POWER

PERSON WITH             -0-

                 8  SHARED DISPOSITIVE POWER

                        2,539,937

9   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                2,539,937

10  CHECK IF THE AGGREGATE AMOUNT IN ROW (9)                  [ ]
    EXCLUDES CERTAIN SHARES*

11  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                2.2%

12  TYPE OF REPORTING PERSON*

                CO
                             *SEE INSTRUCTIONS





                               SCHEDULE 13G

    CUSIP NO. 912909108                                  PAGE 4 OF 11 PAGES


1   NAME OF REPORTING PERSONS.
    I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY).
       APPALOOSA MANAGEMENT L.P.

2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*    (a)  [ ]
                                                         (b)  [ ]

3   SEC USE ONLY

4   CITIZENSHIP OR PLACE OF ORGANIZATION
        DELAWARE


  NUMBER OF      5  SOLE VOTING POWER

   SHARES               -0-

 BENEFICIALLY    6  SHARED VOTING POWER

OWNED BY EACH           6,707,999

 REPORTING       7  SOLE DISPOSITIVE POWER

PERSON WITH             -0-

                 8  SHARED DISPOSITIVE POWER

                        6,707,999

9   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                6,707,999

10  CHECK IF THE AGGREGATE AMOUNT IN ROW (9)                  [ ]
    EXCLUDES CERTAIN SHARES*

11  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                5.9%

12  TYPE OF REPORTING PERSON*

                PN
                             *SEE INSTRUCTIONS



                                SCHEDULE 13G

    CUSIP NO. 912909108                                  PAGE 5 OF 11 PAGES


1   NAME OF REPORTING PERSONS.
    I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY).
       APPALOOSA PARTNERS INC.

2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*    (a)  [ ]
                                                         (b)  [ ]

3   SEC USE ONLY

4   CITIZENSHIP OR PLACE OF ORGANIZATION
        DELAWARE


  NUMBER OF      5  SOLE VOTING POWER

   SHARES               -0-

 BENEFICIALLY    6  SHARED VOTING POWER

OWNED BY EACH           6,707,999

 REPORTING       7  SOLE DISPOSITIVE POWER

PERSON WITH             -0-

                 8  SHARED DISPOSITIVE POWER

                        6,707,999

9   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                6,707,999

10  CHECK IF THE AGGREGATE AMOUNT IN ROW (9)                  [ ]
    EXCLUDES CERTAIN SHARES*

11  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                5.9%

12  TYPE OF REPORTING PERSON*

                CO
                             *SEE INSTRUCTIONS



                                SCHEDULE 13G

    CUSIP NO. 912909108                                  PAGE 6 OF 11 PAGES


1   NAME OF REPORTING PERSONS.
    I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY).
       DAVID A. TEPPER

2   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*    (a)  [ ]
                                                         (b)  [ ]

3   SEC USE ONLY

4   CITIZENSHIP OR PLACE OF ORGANIZATION
        UNITED STATES


  NUMBER OF      5  SOLE VOTING POWER

   SHARES               1,000,000

 BENEFICIALLY    6  SHARED VOTING POWER

OWNED BY EACH           6,707,999

 REPORTING       7  SOLE DISPOSITIVE POWER

PERSON WITH             1,000,000

                 8  SHARED DISPOSITIVE POWER

                        6,707,999

9   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                7,707,999

10  CHECK IF THE AGGREGATE AMOUNT IN ROW (9)                  [ ]
    EXCLUDES CERTAIN SHARES*

11  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                6.8%

12  TYPE OF REPORTING PERSON*

                IN
                             *SEE INSTRUCTIONS






                                SCHEDULE 13G

    CUSIP NO. 912909108                                  PAGE 7 OF 11 PAGES


Item 1.

     (a)  NAME OF ISSUER:

          United States Steel Corporation

     (b)  ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:

          660 Grant Street, Room 1500 
          Pittsburgh, PA 15219-2800

Item 2.

     (a)  NAME OF PERSON FILING:

          This Statement is being filed by and on behalf of Appaloosa
          Investment Limited Partnership I ("AILP"), Palomino Fund Ltd.
          ("Palomino"), Appaloosa Management L.P. ("AMLP"), Appaloosa
          Partners Inc. ("API") and David A. Tepper ("Mr. Tepper" and,
          together with AILP, Palomino, AMLP and API, the "Reporting
          Persons"). Mr. Tepper is the sole stockholder and the President
          of API. API is the general partner of, and Mr. Tepper owns a
          majority of the limited partnership interests in, AMLP. AMLP is
          the general partner of AILP and acts as investment adviser to
          Palomino.

     (b)  ADDRESS OF PRINCIPAL BUSINESS OFFICE:

          The business address of each of the Reporting Persons is c/o
          Appaloosa Management L.P., 26 Main Street, Chatham, NJ 07928.

     (c)  CITIZENSHIP:

          AILP is a Delaware limited partnership. Palomino is a British
          Virgin Islands corporation. AMLP is a Delaware limited
          partnership. API is a Delaware corporation. Mr. Tepper is a
          citizen of the United States.

     (d)  TITLE OF CLASS OF SECURITIES:

          Common Stock, par value $1.00 per share.

     (e)  CUSIP NUMBER: 912909108



                                SCHEDULE 13G

    CUSIP NO. 912909108                                  PAGE 8 OF 11 PAGES


Item 3.   IF THIS STATEMENT IS FILED PURSUANT TO RULES 13d-1(b), OR
          13-2(b), CHECK WHETHER THE PERSON FILING IS A:

     (a)  [ ] Broker or Dealer registered under Section 15 of the Act (15
          U.S.C. 78o);

     (b)  [ ] Bank as defined in Section 3(a)(6) of the Act (15 U.S.C.
          78c);

     (c)  [ ] Insurance Company as defined in Section 3(a)(19) of the Act
          (15 U.S.C. 78c);

     (d)  [ ] Investment Company registered under Section 8 of the
          Investment Company Act (15 U.S.C. 80a-8);

     (e)  [ ] An investment advisor in accordance with Section
          240.13d-1(b)(1)(ii)(E);

     (f)  [ ] An employee benefit plan or endowment fund in accordance with
          Section 240.13d-1(b)(1)(ii)(F);

     (g)  [ ] A parent holding company or control person, in accordance
          with Section 240.13d-1(b)(1)(ii)(G);

     (h)  [ ] A savings association as defined in Section 3(b) of the
          Federal Deposit Insurance Act (12 U.S.C. 1813);

     (i)  [ ] A church plan that is excluded from the definition of an
          investment company under Section 3(c)(14) of the Investment
          Company Act of 1940 (15 U.S.C. 80a-3);

     (j)  [ ] Group, in accordance with Section 240.13d-1(b)(1)(ii)(H)


If this statement is filed pursuant to ss. 240.13d-1(c), check this box. 
     |X|


Item 4.   OWNERSHIP:

          The percentages set forth in this Item 4 are based on there being
          113,691,845 shares of Common Stock outstanding as of October 27,
          2004 as disclosed in United States Steel Corporation's Form 10-Q
          filed on October 29, 2004 for the quarterly period ended
          September 30, 2004.






                                SCHEDULE 13G

    CUSIP NO. 912909108                                  PAGE 9 OF 11 PAGES


     AILP

     (a)  AMOUNT BENEFICIALLY OWNED: 4,168,062

     (b)  PERCENT OF CLASS: 3.7%

     (c)  NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

          (i)  sole power to vote or to direct the vote: -0-

          (ii) shared power to vote or to direct the vote: 4,168,062

          (iii) sole power to dispose or to direct the disposition of: -0-

          (iv) shared power to dispose or to direct the disposition of:
               4,168,062

     Palomino

     (a)  AMOUNT BENEFICIALLY OWNED: 2,539,937

     (b)  PERCENT OF CLASS: 2.2%

     (c)  NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

          (i)  sole power to vote or to direct the vote: -0-

          (ii) shared power to vote or to direct the vote: 2,539,937

          (iii) sole power to dispose or to direct the disposition of: -0-

          (iv) shared power to dispose or to direct the disposition of:
               2,539,937

     AMLP

     (a)  AMOUNT BENEFICIALLY OWNED: 6,707,999

     (b)  PERCENT OF CLASS: 5.9%

     (c)  NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

          (i)  sole power to vote or to direct the vote: -0-






                                SCHEDULE 13G

    CUSIP NO. 912909108                                  PAGE 10 OF 11 PAGES


          (ii) shared power to vote or to direct the vote: 6,707,999

          (iii) sole power to dispose or to direct the disposition of: -0-

          (iv) shared power to dispose or to direct the disposition of:
               6,707,999

     API

     (a)  AMOUNT BENEFICIALLY OWNED: 6,707,999

     (b)  PERCENT OF CLASS: 5.9%

     (c)  NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

          (i)  sole power to vote or to direct the vote: -0-

          (ii) shared power to vote or to direct the vote: 6,707,999

          (iii) sole power to dispose or to direct the disposition of: -0-

          (iv) shared power to dispose or to direct the disposition of:
               6,707,999

     David A. Tepper

     (a)  AMOUNT BENEFICIALLY OWNED: 7,707,999

     (b)  PERCENT OF CLASS: 6.8%

     (c)  NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

          (i)  sole power to vote or to direct the vote: -0-

          (ii) shared power to vote or to direct the vote: 7,707,999

          (iii) sole power to dispose or to direct the disposition of: -0-

          (iv) shared power to dispose or to direct the disposition of:
               7,707,999


Item 5.   OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS:



                                SCHEDULE 13G

    CUSIP NO. 912909108                                  PAGE 11 OF 11 PAGES


          If this statement is being filed to report the fact that as of
the date hereof the reporting person has ceased to be the beneficial owner
of more than five percent of the class of securities, check the following:
|_|

Item 6.   OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON:

          Not applicable.

Item 7.   IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH
          ACQUIRED THE SECURITY BEING REPORTED ON BY THE PARENT HOLDING
          COMPANY:

          Not applicable.

Item 8.   IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP:

          Not applicable.

Item 9.   NOTICES OF DISSOLUTION OF GROUP:

          Not applicable.

Item 10.  CERTIFICATION:

          By signing below I certify that, to the best of my knowledge and
          belief, the securities referred to above were not acquired and
          are not held for the purpose of or with the effect of changing or
          influencing the control of the issuer of the securities and were
          not acquired and are not held in connection with or as a
          participant in any transaction having that purpose or effect.





                               SIGNATURE PAGE

          After reasonable inquiry and to the best of my knowledge and
belief, I certify that the information set forth in this statement is true,
complete and correct.


Dated:   February 1, 2005

                                    APPALOOSA INVESTMENT LIMITED PARTNERSHIP I

                                    By:  APPALOOSA MANAGEMENT L.P.,
                                            Its General Partner

                                            By:  APPALOOSA PARTNERS INC.,
                                              Its General Partner

                                              By:  /s/ David A. Tepper
                                                 --------------------------
                                                      Name:  David A. Tepper
                                                      Title: President

                                    PALOMINO FUND LTD.

                                    By:  APPALOOSA MANAGEMENT L.P.,
                                            Its Investment Adviser

                                            By:  APPALOOSA PARTNERS INC.,
                                              Its General Partner

                                              By:  /s/ David A. Tepper
                                                 --------------------------
                                                      Name:  David A. Tepper
                                                      Title: President

                                    APPALOOSA MANAGEMENT L.P.

                                    By:  APPALOOSA PARTNERS INC.,
                                            Its General Partner

                                              By:  /s/ David A. Tepper
                                               --------------------------
                                                  Name:  David A. Tepper
                                                  Title: President

                                    APPALOOSA PARTNERS INC.

                                    By:  /s/ David A. Tepper
                                       --------------------------
                                        Name:  David A. Tepper
                                        Title:    President

                                    /s/ David A. Tepper
                                    --------------------------
                                    David A. Tepper







                                 EXHIBIT A

                           JOINT FILING AGREEMENT

The undersigned agree that the foregoing Statement on Schedule 13G
(including any and all amendments thereto) is being filed with the
Securities and Exchange Commission on behalf of each of the undersigned
pursuant to Rule 13d-1(k) under the Act and further agree that this Joint
Filing Agreement be included as an Exhibit to such joint filings.

Dated:   February 1, 2005

                                    APPALOOSA INVESTMENT LIMITED PARTNERSHIP I

                                    By:  APPALOOSA MANAGEMENT L.P.,
                                            Its General Partner

                                            By:  APPALOOSA PARTNERS INC.,
                                              Its General Partner

                                              By:  /s/ David A. Tepper
                                                 --------------------------
                                                      Name:  David A. Tepper
                                                      Title: President

                                    PALOMINO FUND LTD.

                                    By:  APPALOOSA MANAGEMENT L.P.,
                                            Its Investment Adviser

                                            By:  APPALOOSA PARTNERS INC.,
                                              Its General Partner

                                              By:  /s/ David A. Tepper
                                                 --------------------------
                                                      Name:  David A. Tepper
                                                      Title: President

                                    APPALOOSA MANAGEMENT L.P.

                                    By:  APPALOOSA PARTNERS INC.,
                                            Its General Partner

                                              By:  /s/ David A. Tepper
                                               --------------------------
                                                  Name:  David A. Tepper
                                                  Title: President

                                    APPALOOSA PARTNERS INC.

                                    By:  /s/ David A. Tepper
                                       --------------------------
                                        Name:  David A. Tepper
                                        Title:    President

                                    /s/ David A. Tepper
                                    --------------------------
                                    David A. Tepper