A fast HMM algorithm is proposed for on-line hand written character recognition. After preprocessing input stroke are discretized so that a discrete HMM is used. This particular discretization naturally leads to a simple procedure for assigning initial state and state transition probabilities. In the training phase, complete marginelization with respect to state is not performed(Constrained Viterbi). A simple smoothing/flooring procedure yields fast and robust learning. A criterion based on normalized maximum likelihood ratio is given for deciding when to create a new model for the same character in the learning phase, in order to cope with stroke order variations and large shape variations. Preliminary experiments are done on the new Kuchibue data base from Tokyo University of Agriculture and Technology. The results seem encouraging.