The combination of classifiers is an established technique to improve the classification performance. The possible combination rules proposed up to now generally try to decrease the classification error rate, which is a performance measure not suitable in many real situations and particularly when dealing with two-class problems. In this case, a good alternative is given by the area under the receiver operating characteristic curve (AUC), whose effectiveness in measuring the classification quality has been proved in many recent papers. In this paper, we propose a method to achieve the optimal linear combination of two dichotomizers based on the maximization of the AUC of the resulting classification system. The effectiveness of the approach has been confirmed by the tests performed on standard datasets.