An iterative algorithm for computing the principal nth root of a positive-definite matrix is presented. The algorithm is based on the Gauss-Legendre approximation of a definite integral. We present a parallelization in which we use as many processors as the order of the approximation. An analysis of the error introduced at each step of the iteration indicates that the algorithm converges more rapidly as the order of the approximation (and thus the number of processors) increases. We describe the results of our implementation of an eight-processor Meiko CS-2, comparing the parallel algorithm to the fastest sequential algorithm, which is the Hoskins-Walton method. (C) 1997 Elsevier Science Ltd.