Fisher optimal discriminant vectors method is an effective method in pattern analysis of high dimension. When the number of the training samples is small compared with the dimensionality of the feature space

the problem becomes the case of a small number of samples. People have proposed many methods for solving the problem of a small number of samples

and made great progress. However

none of the previous methods can obtain the optimal solution when within-class distance equals zero. This point is illustrated in terms of theory

and a new solving method that can obtain the optimal solution in any situations is presented in this paper. The experimental result confirms our inference.