SUPPLEMENT

Exhibit 10.4

EXECUTION VERSION

SUPPLEMENT

SUPPLEMENT (this “Supplement”) dated as of September 20, 2007 among The Nasdaq Stock Market, Inc., a Delaware corporation (“Nasdaq”), and OMX AB, a company duly incorporated and organized under the laws of Sweden (“OMX”).

WHEREAS, on May 25, 2007, Nasdaq and OMX entered into a Transaction Agreement (the “May 25 Agreement”) providing for, among other things, Nasdaq to make a public tender offer to acquire all of the Shares in consideration of a combination of cash and Nasdaq common stock (the “Nasdaq Offer”);

WHEREAS, on May 25, 2007, Nasdaq and OMX issued a press release announcing the terms of the Nasdaq Offer and the recommendation of the OMX Board that OMX shareholders accept the Nasdaq Offer, which recommendation was reiterated by the OMX Board on June 5, 2007;

WHEREAS, on August 9, 2007, Borse Dubai Limited, a company registered in the Dubai International Financial Centre in Dubai with company number 0447 (“Dubai”) announced that it was in the process of purchasing Shares and entering into option arrangements to acquire Shares (the “Dubai Options”);

WHEREAS, on August 17, 2007, Dubai announced (the “Dubai Offer Announcement”) a public tender offer to acquire all of the Shares for SEK 230 in cash (the “Dubai Offer”);

WHEREAS, on September 20, 2007 Nasdaq and Dubai entered into a binding letter agreement (the “Nasdaq Dubai Agreement”) providing for, among other things, (i), subject to the satisfaction of certain conditions, Nasdaq to withdraw the Nasdaq Offer and (ii) Dubai to sell all of the Shares acquired by it in the Dubai Offer and upon exercise of the Dubai Options to Nasdaq, all of the foregoing in accordance with the terms of the Nasdaq Dubai Agreement; and

WHEREAS, the Parties have concluded a Confidentiality Agreement dated March 12, 2007.

NOW THEREFORE, in consideration of the foregoing recitals and the mutual promises hereinafter set forth, the Parties hereto agree as follows:

ARTICLE I

DEFINITIONS AND CONSTRUCTION

Section 1.1 Capitalized terms used but not defined herein shall have the meaning assigned to them in the May 25 Agreement.

Section 1.2 This Supplement only supplements and does not replace the May 25 Agreement. In the event any terms of this Supplement and the May 25 Agreement conflict, it is the intention of the Parties hereto that the terms of this Supplement shall govern the relationship between the Parties.

ARTICLE II

WAIVER

Section 2.1 OMX hereby waives in all respects its rights under the provisions of Section 6 and 7 of the May 25 Agreement with respect to the transactions contemplated by the Nasdaq Dubai Agreement and the sale of the shares by Nasdaq of shares of the London Stock Exchange Group plc and confirms that clause (ii) of Section 7 of the May 25 Agreement was made applicable by virtue of the Dubai Offer.

ARTICLE III

GOVERNANCE

Section 3.1 As of the consummation of the transactions contemplated by the Nasdaq Dubai Agreement, the Nasdaq Board shall consist of sixteen directors, comprised of (a) nine individuals from (or nominated by) the Nasdaq Board as of immediately prior to the consummation of the transactions contemplated by the Nasdaq Dubai Agreement, (b) Nasdaq’s chief executive officer, (c) four individuals from (or proposed for nomination by) the OMX Board as of immediately prior to the consummation of the transactions contemplated by the Nasdaq Dubai Agreement and (c) two individuals proposed for nomination by Dubai immediately prior to the Closing. It is acknowledged and agreed that, with respect to the individuals from (or proposed for nomination by) the OMX Board or by Dubai, (i) all such individuals must be reasonably acceptable to Nasdaq, (ii) with respect to the individuals designated by the OMX Board, three of such individuals must be “independent” for purposes of Nasdaq’s director independence standards, and (iii) with respect to the individuals designated by Dubai, both of such individuals must be “independent” for purposes of Nasdaq’s director independence standards.

Section 3.2 As of the consummation of the transactions contemplated by the Nasdaq Dubai Agreement, (a) OMX may elect to have one-fourth of the members of each committee of the Nasdaq Board be selected from the directors selected from (or proposed for nomination by) the OMX Board as contemplated by Section 3.1, and (ii) Dubai may elect to have one member of the Audit, Executive, Finance, and Management Compensation and Nominating committees of the Nasdaq Board be selected from the directors proposed for nomination by Dubai, in both cases as contemplated by Section 3.1 and subject to applicable law, regulation or stock exchange listing standard.

ARTICLE IV

MISCELLANEOUS

Section 4.1 This Supplement shall terminate upon the earlier of (i) termination of the Nasdaq Dubai Agreement or (ii) termination of the May 25 Agreement. In the event of such termination, this Supplement shall be of no further force or effect, provided, however, that (i) this

2

Section 4.1 and Section 4.9 shall survive the termination of this Supplement and shall remain in full force and effect, and (ii) the termination of this Supplement shall not relieve any party from any liability for any material breach of any warranty, covenant or other provision in this Supplement.

Section 4.2 Each of the Parties to this Supplement confirms that this Supplement represents the entire understanding and constitutes the whole agreement between the Parties in relation to its subject matter and supersedes all prior agreements, covenants, arrangements, communications, representations or warranties, whether oral or written, by any Representative of either of the Parties, except the Confidentiality Agreement dated March 12, 2007 as amended and the May 25 Agreement.

Section 4.3 This Supplement may only be amended by an instrument in writing duly executed by the Parties. No change, termination, modification or waiver of any provision, term or condition of this Supplement shall be binding on the Parties, unless it is made in writing.

Section 4.4 All notices and other communications required or permitted under this Supplement must be in writing and shall be deemed to have been received by a party when: (i) delivered by post, unless actually received earlier, on the third business day after posting, if posted with inland mail, or the fifth Business Day, if posted with international mail; or (ii) delivered by hand, on the day of delivery. All such notices and communications shall be addressed to the Parties’ respective addresses set out in the Introductory section of the May 25 Agreement:

Section 4.5 This Supplement shall be binding upon and inure to the benefit of the successors of the Parties but shall not be assignable by any of the Parties without the prior written consent of the other party.

Section 4.6 The headings in this Supplement are for convenience only and shall not affect the interpretation of any provision of this Supplement.

Section 4.7 This Supplement is not intended to, and does not, confer upon any person other than the Parties hereto any rights or remedies hereunder.

Section 4.8 If any provision of this Supplement or the application of it shall be declared or deemed void, invalid or unenforceable in whole or in part for any reason, the Parties shall amend this Supplement as shall be necessary to give effect to the spirit of this Supplement so far as possible. If the Parties fail to amend this Supplement, the provision which is void, invalid or unenforceable, shall be deleted and the remaining provisions of this Supplement shall continue in full force and effect.

Section 4.9 This Supplement shall be governed by and construed in accordance with the laws of Sweden. Any dispute, controversy or claim arising out of, or in connection with, this Supplement, or the breach, termination or invalidity of this Supplement, shall be settled by arbitration in accordance with the Rules of the Arbitration Institute of the Stockholm Chamber of Commerce. The place of arbitration shall be Stockholm, Sweden. The language to be used in the arbitral proceedings shall be English. The Parties undertake and agree that all arbitral proceedings conducted with reference to this arbitration clause will be kept strictly confidential. This confidentiality undertaking shall cover all information disclosed in the course of such arbitral

3

proceedings, as well as any decision or award that is made or declared during the proceedings. Information covered by this confidentiality undertaking may not, in any form, be disclosed to a third party without the written consent of all Parties hereto. In case this Supplement or any part of it is assigned or transferred to a third party, such third party shall automatically be bound by the provisions of this arbitration clause.

4

This Supplement has been duly executed in two (2) original copies, of which each of the Parties has taken one (1) copy.