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                                                                    EXHIBIT 32.1

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

In connection with the Quarterly Report of Zapata Corporation (the "Company") on
Form 10-Q for the period ending September 30, 2004 as filed with the Securities
and Exchange Commission on the date hereof (the "Report"), Avram A. Glazer, as
Chief Executive Officer of the Company, hereby certifies, pursuant to 18 U.S.C.
Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of
2002 to the best of my knowledge, that:

      (1)   The Report fully complies with the requirements of Section 13(a) of
            the Securities Exchange Act of 1934; and

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

/s/ Avram A. Glazer
- ------------------------------------------------------------
Avram A. Glazer
Chairman of the Board, President and Chief Executive Officer
November 12, 2004

This Certification accompanies this Report pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002 and shall not be deemed filed by the Company for
purposes of Section 18 of the Securities Exchange Act of 1934, as amended.

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