In this paper the problem of nonlinear feature extraction based on the optimization of the Fisher criterion is analyzed. A new nonlinear feature extraction method is proposed. The method does not make use of numerical algorithms and it has an analytical (closed-form) solution. Moreover, no assumptions on the class probability distribution functions are imposed. The proposed method is applied to some standard pattern recognition problems and compared with other classical methodologies already proposed in the literature. The performance of the proposed method turned out to be superior when compared with the other methods studied.