AMENDMENT NO. 2 TO CUSTODIAN AGREEMENT

Exhibit 10.2

AMENDMENT NO. 2 TO CUSTODIAN AGREEMENT

This Amendment No. 2 to the Custodian Agreement dated as of July 30, 2012, is entered into among UNITED STATES COMMODITY INDEX FUNDS TRUST, a Delaware statutory trust (the “Trust”) on its own behalf and on behalf of the United States Commodity Index Fund, United States Copper Index Fund, United States Agriculture Index Fund and United States Metals Index Fund, UNITED STATES COMMODITY FUNDS LLC, a Delaware limited liability company and Sponsor of the Trust (the “Sponsor”), and BROWN BROTHERS HARRIMAN & CO., a limited partnership formed under the laws of the State of New York (“BBH & Co.” or the “Custodian”),

WITNESSETH:

WHEREAS, the Trust, Sponsor and BBH & Co. entered into a Custodian Agreement dated as of July 22, 2010 (the “Agreement”);

WHEREAS, the Agreement was amended by the Trust, Sponsor and BBH & Co. as of December 16, 2010; and

WHEREAS, the Trust, Sponsor and BBH & Co. wish to amend the Custodian Agreement;

NOW, THEREFORE, in consideration of the mutual covenants and agreements herein contained, the Trust, Sponsor and BBH & Co. hereby agree as follows:

Compensation. The Sponsor agrees to pay the Custodian (a) a fee in an amount set forth in the fee letter among the Trust, on its behalf and on behalf of each series therein, the Sponsor and the Custodian in effect on the date hereof or as amended from time to time, and (b) all reasonable out-of-pocket expenses incurred by the Custodian, including the fees and expenses of all Subcustodians, and payable from time to time. The fees paid by the Sponsor to the Custodian will be paid from the Sponsor’s assets. Amounts payable by the Sponsor under and pursuant to this Section 14 shall be payable by wire transfer to the Custodian at BBH & Co. in New York, New York.

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IN WITNESS WHEREOF, each of the parties hereto has caused this Amendment No. 2 to be duly executed as of the date first above written.

UNITED STATES COMMODITY INDEX FUNDS TRUST, on its own behalf and on behalf of the United States Commodity Index Fund, United States Copper Index Fund, United Agriculture Index Fund and United States Metals Index Fund