Exhibit
10.5

    


    AMENDMENT
AGREEMENT

    DATED
AS OF OCTOBER 27, 2008

    TO
THE CUSTODIAN AGREEMENT

    DATED
AS OF MARCH 13, 2008

    


    AMENDMENT AGREEMENT (the
“Amendment”) dated as of October 27, 2008 among BROWN BROTHERS HARRIMAN &
CO.  (“BBH”),
UNITED STATES COMMODITY FUNDS LLC (“USCF”), formerly known as Victoria
Bay Asset Management, LLC, and UNITED STATES HEATING OIL FUND, LP
(“USHO”).

    


    WITNESSETH

     

    The
parties have previously entered into that certain Custodian Agreement dated as
of March 13, 2008 (the “Agreement”).  The parties have agreed to amend
the Agreement in accordance with the terms of this Amendment.

     

     

    NOW, THEREFORE, in consideration of the
mutual agreements herein contained, BBH, USCF and USHO hereby acknowledge and
agree as follows:

     

    


    1.           Amendment of the
Agreement.  Upon execution of this Amendment by BBH, USCF and
USHO, the Agreement shall be hereby amended as follows:

    


    Section 15.1 of the Agreement shall be
deleted in its entirety and replaced with the following:

    


    15.1           Term, Notice and
Effect.  This Agreement shall have an initial term of two (2)
years from the date hereof. Thereafter, this Agreement shall automatically renew
for successive one (1) year periods unless any party terminates this Agreement
by providing written notice no later than seventy-five (75) days prior to the
expiration of the applicable term to the other parties at their address set
forth herein.  Upon the completion of the initial term, either the
Custodian, on the one hand, or the General Partner, on the other hand, may elect
to terminate this Agreement at any time by delivering ninety (90) days notice
thereof to the other party.  

    


    2.          
Representations.  Each
party represents to the other party that:-

    


    (a)           Status.  It is duly
organized and validly existing under the laws of the jurisdiction of its
organization or incorporation and, if relevant under such laws, in good
standing;

    


    (b)           Powers. It has the power to
execute and deliver this Amendment and has taken all necessary action to
authorize such execution, delivery and performance;

    


    (c)           No Violation or Conflict. Such
execution, delivery and performance do not violate or conflict with any law
applicable to it, any provision of its constitutional documents, any order or
judgment of any court or other agency of government applicable to it or any of
its assets or any contractual restriction binding on or affecting it or any of
its assets;

    


    (d)           Consents.  All
governmental and other consents that are required to have been
obtained by it with respect to this Amendment have been obtained and are in full
force and effect and all conditions of any such consents have been complied
with; and

     

    
      
        
        

      

      
        
        

        
          

        

      

      
        
        

      

    

    


    (e)           Obligations
Binding.  Its obligations under this Amendment constitute
its
legal, valid and binding obligations, enforceable in accordance with its
respective terms (subject to applicable bankruptcy, reorganization, insolvency,
moratorium or similar laws affecting creditors’ rights generally and subject, as
to enforceability, to equitable principles of general application (regardless of
whether enforcement is sought in a proceeding in equity or at
law)).

    


    3.           Miscellaneous.

    


    (a)           Entire
Agreement.  The Amendment and the Agreement constitute the
entire agreement and understanding of the parties with respect to its subject
matter and supersedes all oral communication and prior writings (except as other
wise provided herein) with respect thereto.

    


    (b)           Counterparts.  This
Amendment may be signed in any number of counterparts, each of which shall be an
original, with the same effect as if signatures thereto and hereto were upon the
same instrument.

    


    (c)           Headings.  The
headings used in this Amendment are for convenience of reference only and are
not to affect the construction of or to be taken into consideration in
interpreting this Amendment.

    


    (d)           Governing Law.  This
Amendment shall be governed by and construed in accordance with the laws of the
State of New York (without reference to choice of law doctrine).

    


    (e)           Terms. Terms used in this
Amendment, unless otherwise defined herein, shall have the meanings ascribed to
them in the Agreement.

     

    
      
        
        

      

      
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    IN
WITNESS WHEREOF, the parties have caused this Amendment to be executed by their
respective officers or authorized representatives as of the day and year first
above written.

    


    
      
        
          
            
              
                
                  
                    	
                            BROWN
      BROTHERS HARRIMAN & CO.

                          	 
      	
                            UNITED
      STATES COMMODITY FUNDS LLC

                          
	 
      	 
      	 
      
	
                            By:
           /s/ James R.
      Kent

                          	 
      	
                            By:     
      /s/ Howard
      Mah

                          
	
                            Name:
      James R. Kent

                          	 
      	
                            Name: Howard
      Mah

                          
	
                            Title:  
      Managing Director

                          	 
      	
                            Title:   Management
      Director

                          
	
                            Date:  
      October 29, 2008

                          	 
      	
                            Date:  
      October 31, 2008

                          
	 	 	 
	 	 	 
	 	 	UNITED STATES HEATING OIL FUND,
      LP
	 	 	 
	 	 	
                            By:
      United States Commodity Funds LLC, as General Partner

                            


                            By:     
      /s/ Howard
      Mah

                            Name:
      Howard Mah

                            Title:  
      Management Director

                            Date:   October
      31,
2008

                          


                  

                

              

            

          

        

      

    

     

    
      
        
        

      

      
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