Code Excited Linear Prediction(CELP) vocoder exhibits good performance at data rates below 8 kbps. The major drawback of CELP type coders is a large amount of computation. In this paper, we propose a new pitch searching method that preserves the quality of the CELP vocoder reducing computational complexity. The basic idea is that grasps preliminary pitches using the first formant of speech signal and performs pitch search only about the preliminary pitches. As applying the proposed method to the CELP vocoder, we can reduce complexity by 64% in the pitch search.