Abstract: Feature extraction is primary problem of pattern recognition. As one of the most classic methods in the field of feature extraction, Fisher linear discriminant analysis is applied widely. It may meet several possible problems in finding optimal set of discriminant vectors: the components of these vectors may not be real; the eigenvalue may be sensitive; these vectors may not be orthogonal each other. So the balanced scatter matrix is proposed in this paper. Based on the matrix, a discriminant criterion is formed. The optimal set of discriminant vectors can be acquired througn singular value decomposition theorem. The method can avoid the problems metioned above. The result of face recognition experiment shows that it has powerful ability of feature extraction.