EXHIBIT 32.1

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

      The undersigned hereby certify that the Quarterly Report on Form 10-Q for
the quarter ended June 24, 2005 filed by Ameritrade Holding Corporation with the
Securities and Exchange Commission fully complies with the requirements of
Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that
information contained in the report fairly presents, in all material respects,
the financial condition and results of operations of the issuer.

Dated: July 22, 2005                 /s/ Joseph H. Moglia
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                                     Joseph H. Moglia
                                     Chief Executive Officer

Dated: July 22, 2005                 /s/ John R. MacDonald
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                                     John R. MacDonald
                                     Executive Vice President, Chief Financial
                                         Officer and Treasurer