Since the birth of chromosome analysis by the aid of computers, building a fully automated chromosome analysis system has been the ultimate goal. Along with many other challenges, automating chromosome classification and segmentation has been one of the major challenges especially due to overlapping and touching chromosomes. In this paper we present a novel decomposition method for overlapping and touching chromosomes in M-FISH images. To overcome the limited success of previous decomposition methods that use partial information about a chromosome cluster, we have incorporated more knowledge about the clusters into a maximum-likelihood frame work. The proposed method evaluates multiple hypotheses based on geometric information, pixel classification results, and chromosome sizes, and a hypothesis that has a maximum-likelihood is chosen as the best decomposition of a given cluster. About 90% of accuracy was obtained for two or three chromosome clusters, which consist about 95% of all clusters with two or more chromosomes.