Abstract: Linear discriminant analysis often suffers from the small sample size problem when dealing with high dimensional samples.However,a common problem persists for the existing techniques on how to construct a set of complete optimal subspaces and to perform the most efficient discriminant analysis on these constructed subspaces.In this paper,we propose an optimal symmetrical null space analysis to handle this problem.Under the reformulated discriminant criterion,the optimally reduced dimensionality of the sample is discovered to construct a complete subspace where all the discriminative information is included in the two null subspaces of the within-class and between-class matrices and their corresponding orthogonal complement subspaces.As a result,we may overcome the shortcoming that the final dimension of features obtained by Fisher's discriminant analysis is confined by the number of classes.Experimental results conducted on the FERET and ORL face databases demonstrate the effectiveness of the proposed method.