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We have proposed a numerical method for the decomposition of an experimental thermally stimulated depolarization current (TSDC) curve into a sum of elementary spectra obeying the Debye law (a single relaxation time). This method allows one to solve the case of two close overlapping relaxations as well as the case of a distributed relaxation. It consists of fitting the rightmost part of an experimental TSDC curve with a single time relaxation theoretical curve. A new spectrum is obtained by subtracting the theoretical curve from the experimental one. This operation is repeated until the points ordinates of the resulting spectrum are smaller than a fixed limit. The numerical treatment has to always begin with the subtraction of a part, or the whole, of the high temperature relaxation on the decreasing right side of the curve. The probability of an overlap with another relaxation is smaller than elsewhere. We explain how to choose the best fitting curve among all the theoretical curves found. In the particular case of distributed relaxation the decomposition is made by a step method. Our numerical treatment is confronted with experimental results. In the case of the distributed relaxation of an amorphous polymer at glass transition, the decomposition leads to a compensation law. The results are in accordance with those found by fractional polarizations method. © 1998 American Institute of Physics.