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A systematic feature extraction procedure is proposed. It is based on successive extractions of features. At each stage a dimensionality reduction is made and a new feature is extracted. A specific example is given using the Gaussian minus-log-likelihood ratio as a basis for the extracted features. This form has the advantage that if both classes are Gaussianly distributed, only a single feature, the sufficient statistic, is extracted. If the classes are not Gaussianly distributed, additional features are extracted in an effort to improve the classification performance. Two examples are presented to demonstrate the performance of the procedure.