Abstract: In recent works for high performance computing, computation with DNA molecules, that is, DNA computing, has considerable attention as one of nonsilicon based computings. In this paper, we consider three procedures for computing the maximum of Ò binary numbers of Ñ bits, which are represented with Ç´ÑÒµ DNA strands. The first procedure computes the maximum of the binary numbers in Ǵѵ steps using Ç´Òµ kinds of DNA strands. The second and third procedures also compute the maximum in Ç´ÐÓ Òµ and Ç´½µ steps using Ç´ÑÒµ and Ç´ÑÒ¾µ kinds of DNA strands, respectively.