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A new feature extraction criterion, maximum margin criterion (MMC), is proposed in this paper. This new criterion is general in the sense that, when combined with a suitable constraint, it can actually give rise to the most popular feature extractor in the literature, linear discriminate analysis (LDA). We derive a new feature extractor based on MMC using a different constraint that does not depend on the nonsingularity of the within-class scatter matrix Sw. Such a dependence is a major drawback of LDA especially when the sample size is small. The kernelized (nonlinear) counterpart of this linear feature extractor is also established in this paper. Our preliminary experimental results on face images demonstrate that the new feature extractors are efficient and stable.