A new LDA-based face recognition system is presented in this paper. Linear discriminant analysis (LDA) is one of the most popular linear projection techniques for feature extraction. The major drawback of applying LDA is that it may encounter the small sample size problem. In this paper, we propose a new LDA-based technique which can solve the small sample size problem. We also prove that the most expressive vectors derived in the null space of the within-class scatter matrix using principal component analysis (PCA) are equal to the optimal discriminant vectors derived in the original space using LDA. The experimental results show that the new LDA process improves the performance of a face recognition system significantly.