A model-free rank procedure is proposed for the two-population discrimination problem that enables the practitioner to better control the balance between the two probabilities of misclassification. The method is applied to the discriminant functions resulting from normal assumptions and also to an adaptive one which is a weighted average of the linear and quadratic discriminant functions, where the weights are determined from the data. A Monte Carlo study shows that the rank method can greatly improve the balance between the two misclassification probabilities while keeping their average comparatively small.