AMENDMENT NO. 1 TO CUSTODIAN AGREEMENT

Exhibit 10.2

AMENDMENT NO. 1 TO CUSTODIAN AGREEMENT

This Amendment No. 1 to the Custodian Agreement dated as of July 30, 2012, is entered into among UNITED STATES 12 MONTH NATURAL GAS FUND, LP, a limited partnership organized under the laws of the State of Delaware (the “Fund”), UNITED STATES COMMODITY FUNDS LLC, a Delaware limited liability company and General Partner of the Fund (the “General Partner”), 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 Fund, General Partner and BBH & Co. entered into a Custodian Agreement dated as of November 3, 2009 (the “Agreement”); and

WHEREAS, the Fund, General Partner and BBH & Co. wish to amend the Custodian Agreement;

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

Compensation. The General Partner agrees to pay the Custodian (a) a fee in an amount set forth in the fee letter among the Fund, the General Partner 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 General Partner to the Custodian will be paid from the General Partner’s assets. Amounts payable by the General Partner 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. 1 to be duly executed as of the date first above written.

UNITED STATES 12 MONTH NATURAL GAS FUND, LP

By: United States Commodity Funds LLC,

        as General Partner

UNITED STATES COMMODITY FUNDS LLC

BROWN BROTHERS HARRIMAN & CO.