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In the facial expression recognition by analyzing feature-vectors with linear transformation, an accuracy of recognition is depending on expression-classes. The accuracy falls remarkably when feature vectors of expression-classes are linearly nonseparable in a feature space. This paper describes a new method of facial expression analysis and recognition by using nonlinear transformation for separating each expression-classes. Our new method, namely KEMC, consists of the nonlinear transformation defined by kernel functions for transforming higher dimensional space and EMC (eigenspace method based on class features). This paper also shows experimental results of facial expression classification by KEMC.