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                                                                    EXHIBIT 3.4


                           CERTIFICATE OF CORRECTION

                                      OF

                           CERTIFICATE OF AMENDMENT

                                      OF

                         CERTIFICATE OF INCORPORATION

                                      OF

                        AMERITRADE HOLDING CORPORATION


        The undersigned hereby certify that the Certificate of Amendment of the
Certificate of Incorporation of Ameritrade Holding Corporation, a Delaware
corporation (the "Corporation") should be corrected as follows in accordance
with the provisions of Section 103(f) of the Delaware General Corporation Law:

        That Article I of the Certificate of Amendment of the Certificate of
Incorporation of the Corporation as filed on February 26, 1998 incorrectly
stated that Article Fourth of the Certificate of Incorporation was to be amended
and restated in its entirety when it was intended that only the first paragraph
of Article Fourth of the Certificate of Incorporation was to be amended and
restated. Accordingly, Article I of the Certificate of Amendment of the
Certificate of Incorporation of the Corporation is corrected to read as follows:

         That it is advisable and in the best interests of the Corporation that
the first paragraph of Article Fourth of the Certificate of Incorporation be
amended; and that the Directors of the Corporation have duly adopted and
presented to the shareholders entitled to vote thereon the following resolution
setting forth a proposed amendment to the Certificate of Incorporation of such
corporation:

                RESOLVED, that it is advisable and hereby proposed that the
        first paragraph of Article Fourth of the Certificate of incorporation of
        Ameritrade Holding Corporation be revoked and the following be and it 
        hereby is adopted in substitution of the first paragraph of Article 
        Fourth:

                FOURTH: The total number of shares of capital stock which the
        Corporation has authority to issue is 69,000,000 shares, consisting of:

                (1) 3,000,000 shares of Preferred Stock, par value $1.00 per
        share (the "Preferred Stock");

                (2) 60,000,000 shares of Class A Common Stock, par value $.01
        per share (the "Class A Stock"); and



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              (3)   6,000,000 shares of Class B Common Stock, par value $.01 per
share (the "Class B Stock").

              The remainder of Article Fourth as it was originally filed on 
September 25, 1996.

        IN WITNESS WHEREOF, the undersigned Chairman and Chief Executive
Officer and Secretary of Ameritrade Holding Corporation, hereby certify that
the facts hereinabove stated are true and that the execution hereof is their
voluntary act and deed and the voluntary act and deed of said Corporation,
under penalties or perjury of the Corporation, has caused this Certificate of
Correction to be executed this 11th day of December, 1998.






                                     AMERITRADE HOLDING CORPORATION


                                     By /s/ J. Joe Ricketts
                                        ---------------------------------------
                                        J. Joe Ricketts
                                        Chairman and Chief Executive Officer



Attest:


By: /s/ J. Peter Ricketts
   ---------------------------
   J. Peter Ricketts
   Secretary













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