Generating negatively correlated gamma variates using the Beta-Gamma transformation

The Beta-Gamma transform changes a Gamma distributed variate with shape parameter k into a Gamma variate with shape parameter q, where q is less than k. Using this transformation a scheme is given for generating negatively correlated Gamma variates, each with parameter k. The scheme can be implemented with nothing but a generator of Gamma deviates. It requires no inverse probability integral transform for Gamma variates.