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The performance of many state-of-the-art face recognition (FR) methods deteriorates rapidly when large databases are considered. We propose a novel clustering method based on a linear discriminant analysis methodology which deals with the problem of FR on a large-scale database. Contrary to traditional clustering methods such as K-means, which are based on certain "similarity criteria", the proposed method uses a novel "separability criterion" to partition a training set from the large database into a set of K smaller and simpler subsets or maximal-separability clusters (MSCs). Based on these MSCs, a novel two-stage hierarchical classification framework is proposed. Under the framework, the complex FR problem on a large database is decomposed into a set of simpler ones, where traditional methods can be successfully applied. Experiments with a database containing 1654 face images of 157 subjects indicate that the error rate performance of a traditional method under the proposed framework can be greatly improved without significantly increasing computational complexity.