Abstract The performance of the orthonormal discriminant vector (ODV) method is discussed in comparison with discriminant analysis. The ODV method produces the features which maximize the Fisher criterion subject to the orthonormality of features. In contrast with discriminant analysis, the ODV method has no limitation on the maximum number of features to be extracted. From a theoretical viewpoint, it is proved that the ODV method is more powerful than discriminant analysis in terms of the Fisher criterion. The theoretical conclusion is experimentally verified using two real data sets.