A G R E E M E NT

Exhibit 10.2

Execution Copy

AMENDMENT NO. 2 TO RIGHTS AGREEMENT

THIS AMENDMENT (this “Amendment”), dated as of April 22, 2005, is by and between Instinet Group Incorporated, a Delaware corporation (the “Company”), and Mellon Investor Services LLC, a New Jersey limited liability company, as Rights Agent (the “Rights Agent”).

R E C I T A L S

WHEREAS, the Company and the Rights Agent are parties to a Rights Agreement, dated as of May 15, 2001 (the “Rights Agreement”);

WHEREAS, the Company intends to enter into an Agreement and Plan of Merger, dated as of the date hereof (as it may be amended or supplemented from time to time, the “Merger Agreement”) among the Company, The Nasdaq Stock Market, Inc., a Delaware corporation (“Buyer”), and Norway Acquisition Corp, a Delaware corporation and wholly owned subsidiary of Buyer (“Merger Sub”) with respect to a merger of the Company and Merger Sub (the “Merger”);

WHEREAS, the Board of Directors of the Company has approved the Merger Agreement, the Merger and all related agreements; and

WHEREAS, pursuant to Section 27 of the Rights Agreement, for as long as the Rights are then redeemable, the Company may in its sole and absolute discretion, and the Rights Agent shall if the Company so directs, supplement or amend any provision of the Rights Agreement in accordance with the provisions of such section. All acts and things necessary to make this Amendment a valid agreement, enforceable in accordance with its terms, have been done and performed, and the execution and delivery of this Amendment by the Company has been in all respects duly authorized by the Company.

NOW, THEREFORE, in consideration of the foregoing and the mutual agreements set forth in the Rights Agreement and herein, the parties hereto agree as follows:

A G R E E M E N T

NOW, THEREFORE, the Rights Agreement is hereby amended as follows:

1. Amendment of Section 1(a). Section 1(a) of the Rights Agreement is hereby modified and amended by adding the following sentence at the end thereof:

“Notwithstanding anything in this Agreement to the contrary, none of the parties to the Agreement and Plan of Merger, dated as of April 22, 2005, among the Company, The Nasdaq Stock Market, Inc. and Norway Acquisition Corp. (as it may be amended or supplemented from time to time,

and including all exhibits and schedules thereto (the “Merger Agreement”) or any agreements reference therein, as same may be amended or supplemented from time to time), nor any of their Affiliates and Associates, shall be deemed, individually or collectively, to be an Acquiring Person by virtue of (i) the approval, execution or delivery of the Merger Agreement or any related agreements, (ii) the consummation of the Merger (as defined in the Merger Agreement, including any support agreement) or (iii) the consummation of any of the other transactions contemplated by the Merger Agreement and related agreements; provided, however, that nothing contained in this sentence shall prevent any one or more parties to the related agreements (including any support agreement), or any of their Affiliates or Associates, from being deemed an Acquiring Person as a result of the acquisition of additional Common Stock or the taking of any action not contemplated by the Merger Agreement and related agreements (including any support agreement).”

2. Amendment of Section 7(a). Section 7(a) of the Rights Agreement is hereby modified, amended and restated in its entirety as follows:

“Subject to Section 7(e) hereof, at any time after the Distribution Date the registered holder of any Rights Certificate may exercise the Rights evidenced thereby (except as otherwise provided herein including, without limitation, the restrictions on exercisability set forth in Section 9(c), Section 11(a)(ii) and Section 23(a) hereof) in whole or in part at any time after the Distribution Date upon surrender of the Rights Certificate, with the form of election to purchase and the certificate on the reverse side thereof duly executed, to the Rights Agent at the principal office or offices of the Rights Agent designated for such purpose, together with payment of the aggregate Purchase Price with respect to the total number of one one-hundredths of a share (or other securities, cash or other assets, as the case may be) as to which surrendered Rights are then exercisable, at or prior to the earliest of (i) 5:00 P.M., New York City time, on May 15, 2011, or such later date as may be established by the Board prior to the expiration of the Rights (such date, as it may be extended by the Board, the “Final Expiration Date”); (ii) the time at which the right to exercise the Rights terminates pursuant to Section 23 hereof; (iii) the time at which the right to exercise the Rights terminates pursuant to Section 24 hereof; or (iv) the time immediately prior to the Closing of the Merger contemplated by the Merger Agreement (the earliest of (i), (ii), (iii) and (iv) being herein referred to as the “Expiration Date).”

3. Amendment of Section 20. The Rights Agreement is hereby further modified and amended by adding a new Section 20(n) to the end thereof to read in its entirety as follows:

“The Rights Agent shall not be subject to, nor be required to comply with, or determine if any person or entity has complied with, the Merger Agreement or any other agreement between or among the parties thereto, even though reference thereto may be made in this Agreement, or to comply with any notice, instruction,

direction, request or other communication, paper or document other than as expressly set forth in this Agreement.”

4. Amendment of Section 30. Section 30 of the Rights Agreement is hereby modified and amended to add the following sentence at the end thereof:

“Nothing in this Agreement shall be construed to give any holder of Rights or any other Person any legal or equitable rights, remedies or claims under this Agreement by virtue of (i) the approval, execution or delivery of the Merger Agreement or any related agreements, (ii) the consummation of the Merger, (iii) the consummation of any of the other transactions contemplated by the Merger Agreement and related agreements or (iv) the public announcement of any of the foregoing.”

5. Addition of Section 35. The Rights Agreement is hereby further modified and amended by adding a new Section 35 to the end thereof to read in its entirety as follows:

“Section 35. Merger Agreement. Notwithstanding any other provision of this Agreement, neither the approval, execution or delivery of the Merger Agreement, or any related agreement (including any support agreement) nor the consummation of the Merger or other transactions, contemplated by the Merger Agreement is or shall be deemed to be an event described in Section 11(a)(ii) or Section 13 hereof, nor will such performance or consummation result in the occurrence of a Stock Acquisition Date, a Distribution Date or any other separation of the Rights from the underlying Common Stock, nor entitle or permit the holders of the Rights to exercise the Rights or otherwise affect the rights of the holders of the Rights, including giving the holders of the Rights the right to acquire securities of any party to the Merger Agreement.”

6. Addition of Section 36. The Rights Agreement is hereby further modified and amended by adding a new Section 36 to the end thereof to read in its entirety as follows:

“Section 36. Termination of the Agreement. As of the Effective Time (as defined in the Merger Agreement), this Agreement shall terminate and shall forthwith become void and have no effect, without any liability or obligation on the part of the Company, the Rights Agent or the holders of any Rights.”

7. Miscellaneous.

(a) Except as otherwise expressly provided, or unless the context otherwise requires, capitalized terms used herein shall have the respective meanings assigned to them in the Rights Agreement.

(b) This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such State applicable to contracts to be made and performed entirely within such State; provided, however, that all provisions regarding the rights, duties and obligations of the Rights

Agent shall be governed by and construed in accordance with the laws of the State of New York applicable to contracts made and to be performed entirely within such state.

(c) This Amendment may be executed in any number of counterparts, each of which shall for all purposes be deemed to be an original, and all such counterparts shall together constitute one and the same instrument.

(d) If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated. It is the intent of the parties hereto to enforce the remainder of the terms, provisions, covenants and restrictions to the maximum extent permitted by law.

[The remainder of this page has been intentionally left blank]

IN WITNESS WHEREOF, this Amendment has been duly executed by the Company and the Rights Agent as of the day and year first written above.