Traditionally, the strong uncorrelating transformation (SUT) is applied to the zero-lag sample autocovariance and pseudo- autocovariance matrices of the observed mixtures for separating complex-valued stationary sources. The performance of the SUT in that context has been recently analyzed. In this work we extend the analysis to the case where the SUT is applied to "generalized" covariance and pseudo-covariance matrices - which are prescribed by an arbitrary symmetric, positive definite matrix, termed an "association matrix". The analysis applies not only to stationary sources, but also to sources with arbitrary complex-valued temporal covariance and pseudo-covariance. As we show, the use of generalized covariance and pseudo-covariance matrices for the SUT entails a potential for significant improvement in the resulting separation performance, as we also demonstrate in simulation.