A Generalized Nonlinear Discriminant Analysis (GNDA) method is proposed, which implements Fisher discriminant analysis in a nonlinear mapping space. Linear discriminant analysis in the nonlinear mapping space corresponds to nonlinear discriminant analysis in an input space. GNDA suggests a unified framework of nonlinear discriminant analysis which includes the kernel Fisher discriminant analysis as a specific case. Experimental results on UCI data sets demonstrate the validity of our method.