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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                       The Exhibit Index Appears on Page 4


         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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FOR IMMEDIATE RELEASE              Contact:  Cedric Burgher
May 28, 2002                                 Vice President, Investor Relations
                                             713-676-4608

                                             Wendy Hall
                                             Manager, Media Relations
                                             713-676-5227


          HALLIBURTON REPORTS SEC INVESTIGATION OF ACCOUNTING PRACTICE

DALLAS,  Texas -- Halliburton  Company  (NYSE:HAL)  announced  today that it has
received  notification  from the Securities and Exchange  Commission that it has
initiated a preliminary  investigation of the Company's  accounting treatment of
cost  overruns on  construction  jobs.  The Company  expects to receive a formal
request for documents or a subpoena in the next few days.  The Company  believes
that it has  accounted for  construction  claims and change orders in accordance
with generally  accepted  accounting  principles  applicable to the construction
industry.  The Company has advised the SEC that it will cooperate fully with the
SEC in its investigation.

The Company believes that this investigation  results from an article in the New
York  Times  on May  22,  2002,  in  which  certain  allegations  were  reported
concerning the Company's  accounting  treatment of  construction  job claims and
change orders which are negotiated with customers.  Prior to 1998 and the merger
with  Dresser,  the  Company  did not record  such items in revenue or  accounts
receivable before they were resolved with the customer. The Company disclosed in
its Form 10-K for 1998 that it had recorded  losses on certain  engineering  and
construction  projects related to current year claims and change orders which it
did not feel would be accepted by  customers.  Furthermore,  in instances  where
unapproved  claims and change  orders were  recognized  in revenue and  accounts
receivable,  no profits at all were recognized on the related  projects.  During
1998, the Company began to record such items in revenue and accounts  receivable
when the Company  expected such items to be collectible  from the customer.  The
Company has continued this accounting  treatment of similar items since 1998 and
has never  recorded a profit on a job where an unapproved  claim or change order
has been recorded in revenue.



Halliburton,  founded  in  1919,  is one of the  world's  largest  providers  of
products and services to the petroleum and energy industries. The company serves
its  customers  with a broad range of products and  services  through its Energy
Services Group and Engineering and  Construction  Group business  segments.  The
company's World Wide Web site can be accessed at www.halliburton.com.




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