In this paper, westudy the application of an ttMM(hidden Markov model) to the problem of representing protein sequencesby a stochastic motif. Astochastic protein motif represents the small segmentsof protein sequencesthat have a certain function or structure. Thestochastic motif, represented by an HMM,has conditional probabilities to deal withthe stochastic nature of the motif. This HMMdirectly reflects the characteristics of the motif, suchas a protein periodical structure or grouping.In order to obtain the optimal HMM,wedeveloped, the "iterative duplication method' for HMMtopology learning. It starts from a small fully-connected networkand iterates the network generation and parameter optimizationuntil it achievessufficient discrimination accuracy. Usingthis method, weobtained an ttMMfor a leucine zipper motif. Compared to the accuracyof a symbolicpattern representation with accuracy of 14.8 percent, an tIMM achieved 79.3 percent in prediction. Additionally, the methodcan ...