We construct a neural network which can simultaneously approximate several Bayesian and Mahalanobis discriminant functions. The main part of the network is an ordinary one-hidden-layer neural network with a nonlinear output unit, but it has several additional nodes. Since the network has a task to approximate Mahalanobis discriminant functions, the state-conditional probability distributions are supposed to be normal distributions. The method is useful when the Bayesian discriminant functions can be decomposed into sums of a common main part and individual linear additional parts. The main part of the network approximates the quadratic part of the discriminant functions.