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We present a hybrid algorithm for adapting a set of speaker-independent hidden Markov models (HMMs) to a new speaker based on a combination of maximum a posteriori (MAP) parameter transformation and adaptation. The algorithm is developed by first transforming clusters of HMM parameters through a class of transformation functions. Then, the transformed HMM parameters are further smoothed via Bayesian adaptation. The proposed transformation/adaptation process can be iterated for any given amount of adaptation data, and it converges rapidly in terms of likelihood improvement. The algorithm also gives a better speech recognition performance than that obtained using transformation or adaptation alone for almost any practical amount of adaptation data.