In this paper summary, close-form expressions for the bivariate joint probability density function (PDF) and the outage probability (OP) of two-branch selection combining (SC) system in a correlated α-k-μ channel are obtained. The expressions are mathematically tractable, given in terms of well-known functions which are available in common mathematical softwares, and flexible enough to accommodate a myriad of correlation scenarios, useful in the analysis of a more general fading environment. In order to compare the theoretical and simulations results, it is applied the Cholesky decomposition method to correlate the samples with the desired correlation values.