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The purpose of this paper is twofold. First, we derive a necessary and sufficient condition for local synchronization in coupled map lattices (CMLs) with symmetric coupling. In particular, we also identify the best choice of coupling strength in the sense that such a coupling strength gives the fastest convergence rate of initial values toward the synchronous manifold. Furthermore, such a coupling strength is independent of the choice of the individual chaotic map. In addition, it is demonstrated that the wavelet transform method, which is proposed by Wei et al., can greatly increase the applicable ranges of coupling strengths, the parameters of the individual chaotic map, and the number of nodes for local synchronization of CMLs.