A parallel algorithm for computing the singular values of the product of two matrices A and B has been developed. The algorithm is based on the Kogbetliantz method. We use a simple and efficient data distribution, adequate for multicomputers. The application of the rotations is done in a simple order that shows the same convergence rate as the sequential and the odd - even orderings. Also, this convergence is tested in a reliable manner, very easy to implement. On every step of the computation, only a row of A and a column of B are transferred between adjacent processors, and a total interchange of rotation parameters is done in blocks of 2n/p elements. The parallel algorithm has been implemented on a linear ring of T805 transputers using Parallel C, and on a Meiko multicomputer using PVM3, obtaining high efficiencies in both cases.