For SEC Filing Purposes:
						   Filed under Rule 424(b)(3)
				      Registration Nos. 33-54861; 33-54861-01
							33-38505; 33-38505-01

	       PRICING SUPPLEMENT FOR MEDIUM-TERM NOTES, SERIES C
			      (Fixed Rate Only)
Supplement No. 1                                   Dated: March 13, 1995

	 (To Prospectus dated February 3, 1995 and Prospectus Supplement 
			    dated March  8, 1995)

				[UNOCAL LOGO]
			  Union Oil Company of California
			    Medium-Term Notes, Series C
       Payment of Principal, Interest and Premium, if any, Guaranteed by
			      Unocal Corporation
		   Due Nine Months or more from Date of Issue
		   Interest Payable each January 31 and July 31,
       on any Redemption Date, any Repayment Date and the Stated Maturity
                                        
Form:     
	[X]  Book-Entry                    Principal Amount: $5,000,000.00      
	[ ]  Certificated                  Interest Rate:  __7.95__  %
Trade  Date: March 13, 1995                Issue Price:  __100.0__  %
Original Issuance Date: March 20, 1995     Agent's Commissions 
					     or Discounts: __.60__%
Stated Maturity: March 20, 2007            Proceeds to Company:  __99.4_  %
Agent: CS First Boston Corporation
Redemption:                                                     
	[X]     The Note(s) cannot be redeemed prior to maturity                                        
	[ ]     The Note(s) may be redeemed prior to maturity
		Earliest Redemption Date:
		Redemption Price:  __________  %
		Annual Redemption Price Reduction:  __________  %
		Sinking Fund Redemption Dates:
		Sinking Fund Amount:
Repayment:
	[X]     The Note(s) cannot be repaid prior to maturity
	[ ]     The Note(s) may be repaid prior to maturity at the option of 
		the holder
		Repayment Date(s):
		Repayment Price: __________  %

Discount Note:         [ ]  Yes        [X]  No                  
	Total Amount of OID:
	Yield to Maturity:
	Initial Accrual Period:

[ ]     Agent is acting as agent for the sale of Notes at a Price to the 
	Public of (check one)
	[ ]     100% of the Principal Amount
	[ ]     __________ % of the Principal Amount

[ ]     Agent is purchasing the Notes as principal for resale to investors 
	and other purchasers at (check one and complete as necessary):
	[ ]     a fixed public offering price of 100% of the Principal Amount.
	[ ]     a fixed public offering price of  ____________ % of the 
		Principal Amount.
	[ ]     varying prices, related to prevailing market prices at the 
		time of resale, determined by such Agent.

Other Terms (if applicable):