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This correspondence considers the extraction of features as a task of linear transformation of an initial pattern space into a new space, optimal with respect to discriminating the data. A solution of the feature extraction problem is given for two multivariate normal distributed pattern classes using an extended Fisher criterion as the distance measure. The introduced distance measure consists of two terms. The first term estimates the distance between classes upon the difference of mean vectors of classes and the second one upon the difference of class covariance matrices. The proposed method is compared to some of the more popular alternative methods: Fukunaga-Koontz method and Foley-Sammon method.