Exhibit 32.1

                                CERTIFICATION OF
                             CHIEF EXECUTIVE OFFICER
                              OF BMC SOFTWARE, INC.
                       PURSUANT TO 18 U.S.C. Section 1350

      Based on my knowledge, I, Robert E. Beauchamp, Chief Executive Officer of
BMC Software, Inc. (the "Company"), hereby certify that the accompanying report
on Form 10-K for the period ending March 31, 2004 and filed with the Securities
and Exchange Commission on the date hereof pursuant to Section 13(a) of the
Securities Exchange Act of 1934 (the "Report") by the Company fully complies
with the requirements of that section.

      Based on my knowledge, I further certify that the information contained in
the Report fairly presents, in all material respects, the financial condition
and results of operations of the Company.

                                         /s/ ROBERT E. BEAUCHAMP
                                         --------------------------------------
                                         Robert E. Beauchamp
                                         June 14, 2004

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