The auction is a popular way of trading. Despite of the popularity of the auction, only a small number of papers have addressed the protocol which realize the double auction. In this paper, we propose a new method of double auction which improves the algorithm of the existing double auction protocol. Our new method is based on the idea of number comparison which is realized by homomorphic encryption. The new method solves the problem of the privacy of losing bids found in the existing algorithm. The buyers and the sellers can embed a random number in their bidding information by the use of the homomorphic encryption. The players in an auction cannot get anyone else's bidding information. The new method is more efficient than the existing ones. Our new method satisfies the criteria for the auction protocol.