In the paper, it is shown that the error rate of the discriminant analysis can be diminished when restrictions for the parameters are valid. To find suitable restrictions, at first the properties of hierarchical and other multivariate systems are investigated. Then, in a practical section, a modification of the discriminant analysis is offered that consists in decreasing the estimated partial correlations. Finally in the theoretical section, it is veri¬fied that an improvement of the discriminant analysis is attained by a suitable correctionof the positive and negative signs of the discriminant function.