Although the generation of correlated Rayleigh fading envelopes has been intensively considered in the literature, all conventional methods have their own particular shortcomings, which seriously impedes their applicability. A very general, straightforward algorithm is proposed for the generation of an arbitrary number of Rayleigh envelopes with any desired, equal or unequal power in wireless channels, either with or without Doppler frequency shifts. The proposed algorithm can be applied in the case of spatial correlation, such as with antenna arrays in multiple input multiple output (MIMO) systems, or spectral correlation between random processes, as in orthogonal frequency division multiplexing (OFDM) systems. It can also be used for generating correlated Rayleigh fading envelopes in either discrete-time instants or a real-time scenario. Besides being more generalized, our proposed algorithm is more precise, while overcoming all the shortcomings of conventional methods.