SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549



                                    FORM 8-K

                                 CURRENT REPORT

                     PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

                DATE OF REPORT (date of earliest event reported)

                                  MAY 28, 2002

                               Halliburton Company
             (Exact name of registrant as specified in its charter)

State or other                   Commission              IRS Employer
jurisdiction                     File Number             Identification
of incorporation                                         Number

Delaware                         1-3492                  No. 75-2677995

                               3600 Lincoln Plaza
                             500 North Akard Street
                            Dallas, Texas 75201-3391
                    (Address of principal executive offices)

                         Registrant's telephone number,
                       including area code - 214/978-2600






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         INFORMATION TO BE INCLUDED IN REPORT

Item 5.  Other Events

     The registrant may, at its option,  report under this item any events, with
respect to which  information is not otherwise called for by this form, that the
registrant deems of importance to security holders.

     On May 28, 2002  registrant  issued a press release  entitled  "Halliburton
Reports SEC Investigation of Accounting Practice," pertaining to an announcement
that  registrant  has received  notification  from the  Securities  and Exchange
Commission  that it has initiated a preliminary  investigation  of  registrant's
accounting treatment of cost overruns on construction jobs.  Registrant believes
that it has  accounted for  construction  claims and change orders in accordance
with generally  accepted  accounting  principles  applicable to the construction
industry.  Registrant has advised the SEC that it will cooperate  fully with the
SEC in its investigation.

     Please see the full text of the attached press release for further details.

Item 7.  Financial Statements and Exhibits

     List below the financial  statements,  pro forma financial  information and
exhibits, if any, filed as part of this report.

         (c)   Exhibits.

               Exhibit 20 - Press release dated May 28, 2002.




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                                   SIGNATURES

     Pursuant to the  requirements  of the Securities  Exchange Act of 1934, the
registrant  has duly  caused  this  report  to be  signed  on its  behalf by the
undersigned hereunto duly authorized.


                                     HALLIBURTON COMPANY




Date:  May 29, 2002                  By: /s/ Susan S. Keith
                                        ---------------------------------
                                             Susan S. Keith
                                             Vice President and Secretary





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                                  EXHIBIT INDEX



Exhibit                                               Sequentially
Number             Description                        Numbered Page

20                 Press Release of                   5 of 6
                   May 28, 2002
                   Incorporated by Reference











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