In this paper, a novel mathematical model for Enhanced Fisher?s Linear Discriminant is proposed, and it will be referred as EFLD in the following discussion. EFLD has two main advantages: first, it takes both the within-class scatter and the between-class scatter into account as FLD dose; second, it could adaptively distinguish different variables of sample vector according to their scale in statistics. The features extracted by EFLD are much reliable for classification. According to the experiments on Harvard face database and ORL face database, EFLD outperforms some famous algorithms (PCA, FLD and ICA) against large variation in lighting direction, variation in pose and facial expression. EFLD also has another potential contribution to classifying algorithms: there have been a number of classifying algorithms which need FLD to extract classifiable features, some new algorithms could be proposed by replacing FLD by EFLD in algorithms which use FLD to extract features.