CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002




This  certification is provided pursuant to ss. 906 of the Sarbanes-Oxley Act of
2002, 18 U.S.C.  ss. 1350, and  accompanies the Annual Report on Form 10-K/A for
the period ended  December 31, 2003 of  Halliburton  Company (the  "Company") as
filed with the  Securities  and  Exchange  Commission  on the date  hereof  (the
"Report").

I, David J. Lesar, Chief Executive Officer of the Company, certify that:

    (1)   The Report  fully complies with the  requirements of  section 13(a) or
          15(d) of the Securities Act of 1934; and

    (2)   The  information  contained in  the  Report fairly  presents,  in  all
          material   respects,   the   financial   condition   and  results   of
          operations of the Company.


/s/ David J. Lesar
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David J. Lesar
Chief Executive Officer
March 15, 2004