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This paper presents a novel scheme for feature extraction, namely, the generalized two-dimensional Fisher's linear discriminant (G-2DFLD) method and its use for face recognition using multi-class support vector machines as classifier. The G-2DFLD method is an extension of the 2DFLD method for feature extraction. Like 2DFLD method, G-2DFLD method is also based on the original 2D image matrix. However, unlike 2DFLD method, which maximizes class separability either from row or column direction, the G-2DFLD method maximizes class separability from both the row and column directions simultaneously. To realize this, two alternative Fisher's criteria have been defined corresponding to row and column-wise projection directions. Unlike 2DFLD method, the principal components extracted from an image matrix in G-2DFLD method are scalars; yielding much smaller image feature matrix. The proposed G-2DFLD method was evaluated on two popular face recognition databases, the AT&T (formerly ORL) and the UMIST face databases. The experimental results using different experimental strategies show that the new G-2DFLD scheme outperforms the PCA, 2DPCA, FLD and 2DFLD schemes, not only in terms of computation times, but also for the task of face recognition using multi-class support vector machines (SVM) as classifier. The proposed method also outperforms some of the neural networks and other SVM-based methods for face recognition reported in the literature.