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In this paper, an information theoretic approach to selecting feature frames for speaker recognition systems is proposed. A conventional approach in which the frame shift is fixed to around half of the frame length may not be the best choice, because the characteristics of the speech signal may rapidly change, especially at phonetic boundaries. Experimental results show that the recognition accuracy increases if the frame interval is directly controlled using phonetic information. By applying these results to the well-known fact that the recognition accuracy is directly correlated with the amount of mutual information, this paper suggests a novel feature frame selection method for speaker recognition. Specifically, feature frames are chosen to have minimum-redundancy within selected feature frames, but maximum-relevancy to speaker models. It is verified by experiments that the proposed method produces consistent improvement, especially in a speaker verification system. It is also robust against variations in acoustic environment.