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A reasonably large database of online handwritten Bangla characters has been developed. Such a handwritten character sample is composed of one or more strokes. Seventy five such stroke classes have been identified on the basis of the varying handwriting styles present in the character database. Each character sample is a sequence of strokes emanating from these stroke classes. Another database of handwritten Bangla strokes has been developed from the character database. This is the first such database for Bangla script. Certain stroke level features are defined on the basis of certain extremum points which represent the stroke shape reasonably well. The proposed character classification method is a two-stage approach. First, a probability distribution is estimated for each stroke class using the stroke features and then an HMM based character classifier is designed using each stroke class as a state. The parameters of both the stroke class distributions and the character class HMMs are estimated on the basis of the training set having 29,951 character samples. The character level recognition accuracy obtained by the proposed method on the test set having 8,616 samples, is 91.85%.