The correspondence discusses the relationship of the discriminant vector method of feature selection [1] and the method of Kittler and Young [5]. Although both methods determine the feature space coordinate axes by maximizing the generalized Fisher criterion of discriminatory power, with the exception of two class case the resulting feature spaces are considerably different because of the difference in the constraints imposed on the axes by individual methods. It is shown that the latter method is, from the point of view of dimensionality reduction, more powerful and also computationally more efficient.