AMENDMENT TO RIGHTS AGREEMENT

Exhibit 4.1

AMENDMENT TO

RIGHTS AGREEMENT

This AMENDMENT, dated as of January 24, 2007 (the “Amendment”), amends the Rights Agreement, dated as of November 17, 2000 (the “Rights Agreement”), between Teradyne, Inc., a Massachusetts corporation (the “Company”) and Computershare Trust Company, N.A. (as successor to Fleet National Bank), as Rights Agent (the “Rights Agent”). Capitalized terms not defined herein have the definitions assigned to them in Rights Agreement.

WHEREAS, under Section 27 of the Rights Agreement, the Company may from time to time supplement or amend the Rights Agreement without the approval of any holders of Rights Certificates in order to, among other things, change or adopt any provisions with respect to the Rights that the Company may deem necessary or desirable, any such supplement or amendment to be evidenced by a writing signed by the Company and the Rights Agent;

WHEREAS, the Company has determined, and has so directed the Rights Agent, to amend the Rights Agreement as set forth herein pursuant to Section 27 of the Rights Agreement.

NOW, THEREFORE, in consideration of the foregoing and the mutual agreements set forth herein, and intending to be legally bound, the parties hereto agree as follows:

1. The definition of “Final Expiration Date” contained in Section 1 of the Rights Agreement is hereby deleted in its entirety and replaced with the following language:

“FINAL EXPIRATION DATE” shall mean February 8, 2007.

2. Exhibits A and B to the Rights Agreement entitled “Form of Right Certificate” and “Summary of Rights to Purchase Common Shares,” respectively, are hereby amended to replace the words “November 27, 2010” with the words “February 8, 2007” in all places where such words appear.

3. This Amendment shall be deemed to be a contract made under the laws of the Commonwealth of Massachusetts and for all purposes shall be governed by and construed in accordance with the laws of such Commonwealth applicable to contracts to be made and performed entirely within such Commonwealth.

4. All acts and things necessary to make this Amendment a valid agreement, enforceable according to its terms, have been done and performed, and the execution and

delivery of this Amendment by the Company and the Rights Agent have been in all respects duly authorized by the Company and the Rights Agent.

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

6. In all respects not inconsistent with the terms and provisions of this Amendment, the Rights Agreement is hereby ratified, adopted approved and confirmed. In executing and delivering this Amendment, the Rights Agent shall be entitled to all the privileges and immunities afforded to the Rights Agent under the terms and conditions of the Rights Agreement.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed and attested, as of the date first set forth above.