A new implementation of ME (Minimum Error rate) training is proposed. The most important difference from conventional ME training is the use of a trellis-based calculation for the discriminant function, instead of the Viterbi based calculation of the conventional training. The key idea of the training is to use a matrix representation of state transit probabilities of an HMM for calculating the discriminant function so as to simplify the differential operation on the misclassification and loss functions. From the non-segmental characteristics of the discriminant function, loss functions for substitution, insertion and/or deletion errors are easily calculated by substituting, inserting and/or deleting the matrices for the corresponding HMM units of the loss function. Based on the proposed training, therefore, both string level and unit level error minimizations are easily integrated.