CERTIFICATE OF AMENDMENT TO THE 2004 STOCK INCENTIVE PLAN, AS AMENDED OF

EXHIBIT 10.6

CERTIFICATE OF AMENDMENT

TO THE

2004 STOCK INCENTIVE PLAN, AS AMENDED

OF

ARBINET-THEXCHANGE, INC.

The Arbinet-thexchange, Inc. 2004 Stock Incentive Plan (the “Plan”) is hereby amended by the Board of Directors of Arbinet-thexchange, Inc., a Delaware corporation (the “Company”), as follows:

“Initial Grant. Upon the commencement of service on the Board by any individual who is not then an employee of the Company or any subsidiary of the Company, the Company shall grant to such person, and such person shall choose, (i) a Nonstatutory Stock Option to purchase 25,000 shares of Common Stock, (ii) a Restricted Stock Award (as defined in Section 8(a)) for 1,000 shares of Common Stock and a Nonstatutory Stock Option to purchase 22,000 shares of Common Stock, (iii) a Restricted Stock Award for 2,000 shares of Common Stock and a Nonstatutory Stock Option to purchase 19,000 shares of Common Stock, or (iv) a Restricted Stock Award for 3,000 shares of Common Stock and a Nonstatutory Stock Option to purchase 16,000 shares of Common Stock.”

“Annual Grant. Subject to an annual evaluation, which evaluation shall be overseen by the Company’s Nominating and Corporate Governance Committee, on the date of each annual meeting of stockholders of the Company, the Company shall grant to each member of the Board of Directors of the Company who is both serving as a director of the Company immediately prior to and immediately following such annual meeting and who is not then an employee of the Company or any of its subsidiaries, (i) a Nonstatutory Stock Option to purchase no more than 7,000 shares of Common Stock, and (ii) a Restricted Stock Award for no more than 7,000 shares of Common Stock; provided, however, that a director shall not be eligible to receive an option grant or Restricted Stock Award under this Section 6(b) until such director has served on the Board for at least six months.”

“Changes in Capitalization. In the event of any stock split, reverse stock split, stock dividend, recapitalization, combination of shares, reclassification of shares, spin-off or other similar change in capitalization or event, or any distribution to holders of Common Stock other than an ordinary cash dividend, (i) the number and class of securities available under this Plan, (ii) the per-Participant limit set forth in Section 4(b), (iii) the number and class of securities and exercise price per share of each outstanding Option and each Option issuable under Section 6, (iv) the number and class of securities for each Restricted Stock Award issuable under Section 6, (v) the repurchase price per share subject to each outstanding Restricted Stock Award and (vi) the share- and per-share-related provisions of each outstanding Stock Appreciation Right and Other Stock Unit Award, shall be appropriately adjusted by the Company (or substituted Awards may be made, if applicable) to the extent determined by the Board.”

“Upon the occurrence of a Reorganization Event other than a liquidation or dissolution of the Company, except to the extent specifically provided to the contrary in the instrument evidencing any Restricted Stock Award or any other agreement between a Participant and the Company, the repurchase and other rights of the Company under each outstanding Restricted Stock Award shall inure to the benefit of the Company’s successor and shall apply to the cash, securities or other property which the Common Stock was converted into or exchanged for pursuant to such Reorganization Event in the same manner and to the same extent as they applied to the Common Stock subject to such Restricted Stock Award.”