Dynamic programming offers the advantage of being able to determine an optimal match of an unknown pattern against known templates. One of disadvantage of dynamic programming is its computational intensity. This thesis proposes a local dynamic programming technique which saves the computational burden of full dynamic programming yet yields the optimal match with utterance of high probability, which is segmented on the basis of acoustic similarity of speech signal. The local dynamic programming performs the dynamic time warping on the segment unit instead of the whole frames of the utterance. Also by using the branch and bound search technique which include the pruning method it is possible to reduce the search space.