Linear discriminant analysis (LDA) has been successfully applied into computer vision and pattern recognition for effective feature extraction. High-dimensional objects such as images are usually transform as 1D vectors before the LDA transformation. Recently, two-dimension LDA (2DLDA) methods have been proposed which reduced the dimensionality of images without transforming the matrices into vectors. However, the objective function for 2DLDA remains an unresolved problem. In this paper, we (1) propose a symmetric LDA formulation which resolves the ambiguity problem, and (2) propose an effective algorithm to solve the symmetric 2DLDA objective. Experiments on UMIST, CMU PIE, and YaleB images databases show that our approach outperforms the other 2DLDA methods in terms of both classification accuracy and objective function results.