One limitation of vector-based LDA and its matrix-based extension is that they cannot deal with heteroscedastic data. In this paper, we present a novel two-dimensional feature extraction technique for face recognition which is capable of handling the heteroscedastic data in the dataset. The technique is a general form of two-dimensional linear discriminant analysis. It generalizes the interclass scatter matrix of two-dimensional LDA by applying the Chernoff distance as a measure of separation of every pair of clusters with the same index in different classes. By employing the new distance, our method can capture the discriminatory information presented in the difference of covariance matrices of different clusters in the datasets while preserving the computational simplicity of eigenvalue-based techniques. So our approach is a proper technique for high-dimensional applications such as face recognition. Experimental results on CMU-PIE, AR and AT & T face databases demonstrate the effectiveness of our method in term of classification accuracy.