SummaryThe Rayleigh distribution is of paramount importance in signal processing and many other areas, yet an expression for random variables of arbitrary dimensions has remained elusive. In this note, we generalise the results of Beard and Tekinay for quadrivariate random variables to cases of unconstrained order and provide a simple algorithm for evaluation. The assumptions of cross‐correlation between in‐phase and quadrature, as well as nonsingularity of the covariance matrix, are retained throughout our computations.