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Abstract: The complete linear discriminant analysis (CLDA) algorithm has been successfully employed for face recognition. The CLDA method can make full use of the discriminant information of the training samples. However, CLDA suffers from the scalability problem. In this paper, we propose an incremental CLDA (ICLDA) to overcome this limitation. We first propose a new implementation of CLDA in which two steps of QR decomposition, rather than singular value decomposition (SVD), are used to get the orthonormal bases of the range and null spaces of the within-class scatter matrix. Then, by using efficient QR-updating technique, we propose the ICLDA method which can accurately incrementally update the discriminant vectors of CLDA instead of recomputing the CLDA again. Experiments on PIE and FERET face databases show the efficiency of our proposed CLDA algorithms over the original implementation of CLDA. [Copyright &y& Elsevier]