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                                                                    EXHIBIT 10.4

                  AMENDMENT NUMBER ONE TO EMPLOYMENT AGREEMENT

      This Amendment Number One to Employment Agreement is entered into as of
the 24th day of April, 2008, by and between TD Ameritrade Holding Corporation
(the "Company") and T. Christian Armstrong ("Executive") (collectively referred
to as the "Parties").

      WHEREAS, Executive and Company entered into an Employment Agreement dated
May 23, 2006 (the "Employment Agreement"); and

      WHEREAS, Executive and Company desire to modify certain of the terms and
conditions of Executive's employment relationship, as originally provided
pursuant to the Employment Agreement;

      NOW, THEREFORE, in consideration of the promises made herein, the Parties
hereby agree as follows:

      (Capitalized terms shall have the meanings ascribed them in the Employment
Agreement)

      1. Termination of Employment. Executive's employment with the Company will
terminate on March 1, 2009, the expiration of the Initial Term (the "Termination
Date"), subject to receipt of Executive's written notice of non-renewal and
voluntary resignation at least sixty (60) days prior to the Termination Date.

      2. Position and Duties. Executive will continue in the same position and
perform the same duties as contemplated by Section 1(a) of the Employment
Agreement through the Termination Date or until such earlier date as may be
determined by the Company in its sole discretion in the event that the Company
earlier retains a replacement for Executive. In the event of such earlier
replacement date, Executive will, following conclusion of a mutually agreed
transition period, assume a modified advisory/special projects position
reporting to the Company's Chief Executive Officer and will remain in that
modified position from such earlier replacement date through the Termination
Date.

      3. Consideration. The Company agrees that Executive shall be entitled to
the following:

            (a) Base Salary. Executive will continue to receive the Base Salary
specified in Section 4(a) of the Employment Agreement through the Termination
Date, as well as all other applicable amounts contemplated by Section 7 of the
Employment Agreement as of the Termination Date.

            (b) Annual Incentive. Executive will continue to be eligible for the
Annual Incentive specified in Sections 4(b) of the Employment Agreement,
provided that (i) the Annual Incentive for the period beginning on October 1,
2008 shall be pro-rated, calculated based on the Target, through the Termination
Date; (ii) both the Annual Incentive for the current fiscal year and the
pro-rata Annual Incentive for the period beginning on October 1, 2008 shall be
paid entirely in cash; and (iii) the Annual Incentives shall be paid at the same
time as such other annual incentives are made to the Company's other executive
officers following the Termination Date and the completion of the applicable
performance period.

            (c) Annual Award. Executive will continue to be eligible for the
Annual Award contemplated by Section 4(c)(ii) of the Employment Agreement,
provided that (i) the Annual

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Award for the period beginning on October 1, 2008 shall be pro-rated, calculated
based on the Target, through the Termination Date; (ii) both the Annual Award
for the current fiscal year and the pro-rata Annual Award for the period
beginning on October 1, 2008 shall be paid entirely in cash; and (iii) the
Annual Awards shall be paid at the same time as such other payments are made to
the Company's other executive officers following the Termination Date and the
completion of the applicable performance period.

            (d) Stock. Executive's vesting and settlement with respect to those
unvested equity awards outstanding as of the Termination Date shall continue to
be subject to all the terms and conditions of the Restricted Stock Unit
Agreements and Plan.

      Executive acknowledges that the foregoing consideration is subject to
execution of a separation and release agreement as further described in Section
9(a) of the Employment Agreement and Executive expressly agrees to sign and not
revoke a separation and release agreement, in substantially the form attached as
Exhibit A to the Employment Agreement, which separation and release agreement
will be provided to Executive on or before the Termination Date.

      4. Waiver of Additional Payments and Rights. Executive acknowledges,
understands and hereby agrees to waive any right to any additional compensation,
benefits, severance or any additional Annual Incentive and/or Annual Award,
other than that compensation, benefits, severance and pro-rata portion of the
Annual Incentive and Annual Award as specified in the Amendment, including
specifically any compensation or benefits as originally specified in Section 8
of the Employment Agreement. Executive also acknowledges, understands and hereby
agrees that neither the modification to his position prior to the Termination
Date contemplated by Section 2 of this Amendment nor the execution of this
Amendment shall be considered grounds to constitute Good Reason pursuant to
Section 8 of the Employment Agreement.

      Except as expressly amended and supplemented hereby, the Employment
Agreement shall remain in full force and effect. In the event of any conflict
between the terms and conditions of this Amendment and the terms and conditions
of the Employment Agreement, this Amendment shall prevail.

      IN WITNESS WHEREOF, the Parties have executed this Amendment on the
respective dates set forth below:

                                   TD AMERITRADE HOLDING CORPORATION

Dated:  April 24, 2008             By: /s/ K. GANZLIN
                                       ------------------------------------
                                   Name: K. Ganzlin
                                   Title: Chief Human Resources Officer

                                   T. Christian Armstrong, an individual

Dated:  April 24, 2008             /s/ T. CHRISTIAN ARMSTRONG
                                   -----------------------------------------