In a large vocabulary speech recognition system, it is desirable to make use of previously acquired speech data when encountering new speakers. We describe an adaptation strategy based on a piecewise linear mapping between the feature space of a new speaker and that of a reference speaker. This speaker-normalizing mapping is used to transform the previously acquired parameters of the reference speaker onto the space of the new speaker. This results in a robust speaker adaptation procedure which allows for a drastic reduction in the amount of training data required from the new speaker. The performance of this method is illustrated on an isolated utterance speech recognition task with a vocabulary of 20,000 words.