This paper addresses the issue of learning hidden Markov model (HMM) parameters for speaker-independent continuous speech recognition. Bahl et al. [1] introduced the corrective training algorithm for speaker-dependent isolated word recognition. Their algorithm attempted to improve the recognition accuracy on the training data. In this work, we extend this algorithm to speaker-independent continuous speech recognition. We use cross-validation to increase the effective training size. We also introduce a near-miss sentence hypothesization algorithm for continuous speech training. The combination of these two approaches resulted in over 20% error reductions both with and without grammar.