Assume that a matrix X : p × n is matrix normally distributed and that the Kolmogorov condition, i.e., limn,p→∞ n = c > 0, holds. We propose a test for identity of the covariance matrix using a goodness-of-fit approach. Calculations are based on a recursive formula derived by Pielaszkiewicz et al. The test performs well regarding the power compared to presented alternatives, for both c < 1 or c ≥ 1.