In terms of the large-sample joint distribution of Z, the \(2^{-1}p(p- 1)\) Fisher z-transforms of the elements in a \(p\times p\) correlation matrix, the authors prove that the variance matrix of Z has just three projector matrices in its spectral decomposition under the hypothesis of equal population correlations. This results in a natural partition for the large-sample chi-squared test for equality of correlations. A linear model is discussed and a simple example is also given.