The multivariate Rayleigh distribution is of crucial importance to many applied problems of engineering, such as in the analysis of multi-antenna wireless systems. Due to the lack of a generalised closed form of the distribution, the dependence on effective approximation methods for evaluation has created numerous numerical approaches with considerable restrictions in both dimensionality, as well as the structure of covariance matrices. In this paper we extend a previously introduced method [1] without either of these limitations. We then compare the performance of the new algorithms to recent integration methods of fixed dimension, presented by Beaulie and Zhang [2] and highlight the advantages of the new method.