In genetic experiments in which variance components are to be estimated from correlated mean squares and mean products, the direct computation of iterative weighted least squares estimates is computationally expensive. An algorithm has been developed which finds and applies linear transformations to the input matrices of mean squares and mean products such that the transformed mean squares and mean products are approximately uncorrelated. A test for convergence uses the fact, apparently previously unnoticed, that the weighted "regression" sum of squares converges to a constant depending only on the order and degrees of freedom of the input matrices of mean squares and mean products.