Discriminative training for hidden Markov models (HMMs) has been a central theme in speech recognition research for many years. One most popular technique is minimum classification error (MCE) training, with the objective function closely related to the empirical error rate and with the optimization method based traditionally on gradient descent. In this paper, we provide a new look at the MCE technique in two ways. First, we develop a non-trivial framework in which the MCE objective function is re-formulated as a rational function for multiple sentence-level training tokens. Second, using this novel re-formulation, we develop a new optimization method for discriminatively estimating HMM parameters based on growth transformation or extended Baum–Welch algorithm. Technical details are given for the use of lattices as a rich representation of competing candidates for the MCE training.