Code Excited Linear Prediction(CELP) speech coders exhibit good performance at data rates below 4.8 kbps. This major drawback of CELP type coders is required much computation. In this paper, we propose a new pitch search method that preserves the quality of the CELP vocoder with reducing complexity. In the pitch searching, we detect the segments of high correlation by a simple preprocessing, and then carry out the pitch searching only for the segments obtained by the preprocessing. By using the proposed method, we can get approximately $77\%$ complexity reduction in the pitch search.