THE NASDAQ STOCK MARKET, INC.

EXHIBIT 4.1

EXECUTION COPY

THE NASDAQ STOCK MARKET, INC.

TO

LAW DEBENTURE TRUST COMPANY OF NEW YORK,

as Trustee

FIRST SUPPLEMENTAL INDENTURE

Dated as of

December 8, 2005

TO

INDENTURE

Dated as of

April 22, 2005

3.75% Convertible Notes due 2012

FIRST SUPPLEMENTAL INDENTURE

THIS FIRST SUPPLEMENTAL INDENTURE (the “First Supplemental Indenture”), dated as of December 8, 2005, between The Nasdaq Stock Market, Inc., a Delaware corporation (hereinafter called the “Company”), having its principal office at One Liberty Plaza, New York, NY 10006 and Law Debenture Trust Company of New York, as trustee under the Original Indenture hereinafter referred to (hereinafter called the “Trustee”).

WITNESSETH

WHEREAS, the Company has heretofore executed and delivered an indenture, dated as of April 22, 2005 (the “Original Indenture”), between the Company and the Trustee, pursuant to which the Company has issued $205,000,000 aggregate principal amount of its 3.75% Series A Convertible Notes due 2012 (the “Series A Notes”) and $240,000,000 aggregate principal amount of its 3.75% Series B Convertible Notes due 2012 (the “Series B Notes”, together with the Series A Notes, the “Notes”);

WHEREAS, the Company seeks to increase the maximum amount of Designated Senior Indebtedness that it may incur in connection with the Credit Facility;

WHEREAS, Section 11.02 of the Original Indenture provides that, with the consent (evidenced as provided in Article 9 of the Original Indenture) of the holders of a majority in aggregate Principal Amount of the Notes at the time outstanding, the Company, when authorized by resolutions of the Board of Directors, and the Trustee may enter into an indenture supplemental to the Original Indenture for the purpose, among other things, of changing in any manner any of the provisions of the Original Indenture or modifying in any manner the rights of the holders of the Notes as in said Section provided;

WHEREAS, holders holding not less than a majority in aggregate Principal Amount of the outstanding Notes have, pursuant to Section 11.02 of the Original Indenture, consented to the amendment to the Original Indenture as set forth herein and to the execution and delivery of this First Supplemental Indenture by the Trustee;

WHEREAS, the Company has delivered to the Trustee resolutions of the Board of Directors of the Company authorizing the execution and delivery of this First Supplemental Indenture;

WHEREAS, the Company has filed with the Trustee consents (evidenced as provided in Article 9 of the Indenture) of the requisite percentage of holders in aggregate Principal Amount of the outstanding Notes to the amendment of the Original Indenture as set forth herein and to the execution and delivery of this First Supplemental Indenture by the Trustee;

WHEREAS, the Company has requested the Trustee to join it in the execution and delivery of this First Supplemental Indenture; and

WHEREAS, all conditions precedent related to the entering of this First Supplemental Indenture have been satisfied.

NOW, THEREFORE, in consideration of the premises and for other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the Company and the Trustee for the benefit of each other and for the equal and proportionate benefit of the holders of the Notes agree as follows:

ARTICLE 1

DEFINITIONS

Terms used herein and not otherwise defined shall have the meanings ascribed to such terms in the Original Indenture.

ARTICLE 2

AMENDMENT OF THE INDENTURE

Section 3.01. Amendment of Definitions. Subject to Article 3 hereof, the Original Indenture is hereby amended by amending the definition of “Credit Facility” in Article 1 by replacing “$800,000,000” with “$825,000,000”.

ARTICLE 3

EFFECTIVENESS OF AMENDMENT

Upon the execution and delivery of this First Supplemental Indenture by the Company and the Trustee, this First Supplemental Indenture shall become effective and the Original Indenture shall be amended and supplemented in accordance herewith, and the rights of the holders of the Notes modified hereby, and this First Supplemental Indenture shall form a part of the Original Indenture for all purposes, and every holder of Notes authenticated and delivered under the Original Indenture shall be bound hereby.

ARTICLE 4

MISCELLANEOUS

Section 4.01. Execution as Supplemental Indenture. This First Supplemental Indenture is executed and shall be construed as an indenture supplemental to the Original Indenture and, as provided in the Original Indenture, this First Supplemental Indenture forms a part thereof. Except as herein expressly otherwise defined, the use of the terms and expressions herein is in accordance with the definitions, uses and constructions contained in the Original Indenture.

Section 4.02. No Other Amendments. Except as expressly amended hereby, the Original Indenture shall continue in full force and effect in accordance with the provisions thereof.

Section 4.03. Trustee. The recitals contained herein are those of the Company and not the Trustee, and the Trustee assumes no responsibility for the correctness of same. The Trustee makes no representations as to the validity or sufficiency of this First Supplemental Indenture. All rights, protections, privileges, indemnities and benefits granted or afforded to the Trustee under the Original Indenture shall be deemed incorporated herein by this reference and shall be deemed applicable to all actions taken, suffered or omitted by the Trustee under this First Supplemental Indenture.

Section 4.04. Provisions Binding on the Company’s Successors. Any covenants and agreements contained in this First Supplemental Indenture made by the Company shall bind its successors and assigns whether so expressed or not.

Section 4.05. Governing Law. This First Supplemental Indenture shall be deemed to be a contract made under the laws of the State of New York, and for all purposes shall be construed in accordance with the laws of the State of New York (including Section 5-1401 of the New York General Obligations Law or any successor to such statute).

Section 4.06. Execution and Counterparts. This First Supplemental Indenture may be executed in any number of counterparts, each of which when so executed shall be deemed to be an original, but all such counterparts shall together constitute one and the same instrument.

Section 4.07. Headings. The article and section headings herein are for convenience only and shall not affect the construction hereof.

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IN WITNESS WHEREOF, the parties hereto have caused this First Supplemental Indenture to be duly executed as of the date first written above.