Class overlapping and highly unequal class sizes can make very difficult the successful construction of a classification system. However, this situation is not infrequent in practical settings, one of them certainly being credit card fraud prevention. In this paper we will examine a new procedure, which we call Nonlinear Discriminant Analysis (NLDA), for classifier construction in such cases that combines the excellent approximation properties of the well-known Multilayer Perceptrons with the target–free classical discrimination technique of Fisher’s Analysis. Besides a description of NLDA fundamentals, we will illustrate the better performance in the above situations of the resulting classifiers, both in an experimental setting and upon the concrete problem of credit card fraud detection.