Summary: In this article we show that the Kullback's statistic for testing equality of several correlation matrices may be considered a modified likelihood ratio statistic when sampling from multivariate normal populations. We derive the asymptotic null distribution of \(L^\ast\) in series involving independent chisquare variables by expanding \(L^\ast\) in terms of other random variables and then inverting the expansion term by term. An example is also given to exhibit the procedure to be used when testing the equality of correlation matrices using the statistic \(L^\ast\) .