This paper describes a new algorithm for sentence error minimisation training of phoneme based HMM speech recognition systems. The important aspect of this work is that the minimisation criterion is chosen to directly minimise those errors observable to the final user(2,e. sentence errors), not errors resulting simply as a consequence of the choice of classifier structure, e. phoneme errors). The recognition performance of the resulting minimum error(ME) HMMs is compared against that of standard maximum likelihood(ML) trained models. In every performance measure made the ME HMMs proved superior.