AMENDMENT TO RIGHTS AGREEMENT

Exhibit 4.2

AMENDMENT TO RIGHTS AGREEMENT

This Amendment to Rights Agreement, effective as of 12 noon on December 1, 2008, is between Convergys Corporation, an Ohio corporation (the “Corporation”), and Computershare Trust Company, N.A., (the “Rights Agent”).

R E C I T A L S:

WHEREAS, on November 19, 1998, the Board of Directors of Convergys Corporation adopted a Rights Agreement, effective and dated as of November 30, 1998, between Convergys Corporation and Computershare Trust Company, N.A. (as successor Rights Agent for the Fifth Third Bank, N.A.),

WHEREAS, on November 19, 1998, the Board of Directors declared a dividend distribution of one right (“Right”) on each of the Company’s outstanding Common Shares, without par value (the “Common Shares”), to holders of record of the Common Shares at the close of business on December 1, 1998, and well as to each Common Share issued after December 1, 1998,

WHEREAS, the Rights and the Rights Agreement are set to expire at the close of business on December 1, 2008,

WHEREAS, Section 27 of the Rights Agreement provides that the Company may supplement or amend any provision of the Rights Agreement;

WHEREAS, the Board of Directors of the Corporation has determined to amend the Rights Agreement as follows, effective prior to the expiration of Rights Agreement.

NOW THEREFORE, for valuable consideration, the sufficiency of which is acknowledged by the parties hereto, the following has been agreed:

1. Term.

(a) The term of the Rights Agreement is extended until the close of business on June 30, 2009.

(b) The reference to “December 1, 2008” appearing in the legend set forth in Section 3(c) is hereby amended to be a reference to “June 30, 2009,” and any certificate previously issued with a legend referring to December 1, 2008 shall be deemed to refer to June 30, 2008, notwithstanding the reference to such earlier date.

(c) “Final Expiration Date” means the close of business on June 30, 2009.

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2. Notice to Rights Agent. Section 2 of the Rights Agreement is hereby amended to add the following new language at the end of the last sentence thereof:

“, upon ten (10) days’ prior written notice to the Rights Agent. The Rights Agent shall have no duty to supervise, and shall in no event be liable for, the acts or omissions of any such co-Rights Agent.”

3. Countersignature. Section 5 of the Rights Agreement is hereby amended to delete the second sentence thereof in its entirety and replace it with the following:

“The Rights Certificates shall be countersigned by the Rights Agent, either manually or by facsimile signature, and shall not be valid for any purpose unless so countersigned.”

4. Transfer Agency Relationship. Section 21 of the Rights Agreement is hereby amended as follows:

(a) to insert the following new sentence after the existing first sentence thereof:

“In the event the transfer agency relationship in effect between the Company and the Rights Agent terminates, the Rights Agent will be deemed to have resigned automatically and be discharged from its duties under this Agreement as of the effective date of such termination, and the Company shall be responsible for sending any required notice.”; and

(b) to delete the term “$100 million” and replace it with “$50 million.”

5. Notice. Section 26 of the Rights Agreement is hereby amended to delete the Rights Agent address information in its entirety and replace it with the following:

Computershare Trust Company, N.A.

250 Royall Street

Canton, MA 02021

Attention: Client Services

6. Force Majeure. The Rights Agreement is hereby amended to insert a new Section 35, as follows:

“35. Force Majeure. Notwithstanding anything to the contrary contained herein, the Rights Agent shall not be liable for any delays or failures in performance resulting from acts beyond its reasonable control including, without limitation, acts of God, terrorist acts, shortage of supply, breakdowns or malfunctions, interruptions or malfunction of computer facilities, or loss of data due to power failures or mechanical difficulties with information storage or retrieval systems, labor difficulties, war, or civil unrest.”

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7. Defined Terms. The terms as defined in the Rights Agreement, other than as modified in this Agreement, shall continued to have the meanings ascribed to them in the Rights Agreement. Any defined term used herein, unless expressly stated otherwise in this Agreement, shall have the meaning ascribed to them in the Rights Agreement,

8. Controlling Agreement. In the even of any conflict between the terms of this Agreement and the Rights Agreement, this Agreement shall control.

9. Benefit of this Agreement. Nothing in this Agreement shall be construed to give to any Person other than the Corporation, the Rights Agent and the registered holders of the Right Certificates (and, prior to the Distribution Date, registered holders of the Common Shares) any legal or equitable right, remedy or claim under this Agreement; but this Agreement shall be for the sole and exclusive benefit of the Corporation, the Rights Agent and the registered holders of the Right Certificates (and, prior to the Distribution Date, registered holders of the Common Shares).

10. Severability. If any term, provision, covenant or restriction of this Agreement 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 Agreement shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

11. Governing Law. This Agreement, each Right and each Right Certificate issued hereunder shall be deemed to be a contract made under the laws of the State of Ohio and for all purposes shall be governed by and construed in accordance with the laws of Ohio applicable to contracts made and to be performed entirely within such State.

[This Area Intentionally Left Blank]

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IN WITNESS HEREOF, the parties hereto have caused this amendment to the Rights Agreement to be duly executed and their respective corporate seals to be hereunto affixed and attested, all as of the day and year first above written.

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