In the paper, a new method for computing weighted distances for Dynamic Time Warping based speaker verification systems is described. Weighted distances use coefficients determined usually globally and this, of course, does not consider the phonetic content of the vocal pattern. The goal of local weighting is to connect the computation of the weights to the phonetic events occurring in the patterns in order to compute a weighting matrix for each phonetic event. This is approximately achieved, in the work described in this paper, by using the DTW optimum path obtained during the comparison of two reference patterns. The method has been simulated on a VAX computer, and an accuracy improvement with respect to the global case has been observed.