In the past several years, we’ve been studying feature transformation (FT) approaches to robust automatic speech recognition (ASR) which can compensate for possible “distortions” caused by factors irrelevant to phonetic classification in both training and recognition stages. Several FT functions with different degrees of flexibility have been studied and the corresponding maximum likelihood (ML) training techniques developed. In this paper, we study yet another new FT function which takes the most flexible form of frame-dependent linear transformation. Maximum a posteriori (MAP) estimation is used for estimating FT function parameters to deal with the possible problem of insufficient training data caused by the increased number of model parameters. The effectiveness of the proposed approach is confirmed by evaluation experiments on Finnish Aurora3 database.