This paper presents a new feature representation method, named two- dimensional orthogonalized Fisher discriminant analysis(2D-OFD). The method adopts the 2D-LDA and orthogonalization of Fisher vector. It produces the small size scatter matrix than 1D method. Therefore it can evaluate the scatter matrix accurately. In addition, it is not suffered from small sample size problem. The orthogonalization eliminates the linear dependences among Fisher's discriminant vectors. As a result, it promotes the discriminant capability of the 2D-LDA. The proposed method is tested on the ORL face image database. We test our method 10 times. For each experiment, five training images are randomly chosen each person and the other five images are used for testing. The test show that the average recognition rate is 96.2%. When the image is downsampled to 28x23 matrix to reduce the computational complexity, the average recognition rate is 95.9%.