In this paper an exact and complete analysis of the Lloyd–Max's algorithm and its initialization is carried out. An effective method for initialization of Lloyd–Max's algorithm of optimal scalar quantization for Laplacian source is proposed. The proposed method is very simple method of making an intelligent guess of the starting points for the iterative Lloyd–Max's algorithm. Namely, the initial values for the iterative Lloyd–Max's algorithm can be determined by the values of compandor's parameters. It is demonstrated that by following that logic the proposed method provides a rapid convergence of the Lloyd–Max's algorithm.