In this paper, a classifier based on the positive Boolean function (PBF) is proposed for the supervised pattern classification. A PBF is exactly represented as one sum-of-product form without any negative components. The PBF possesses the well-known threshold decomposition and stacking properties. The classification errors can be calculated from the summation of the absolute errors incurred at each level. The optimal PBF are found and designed to be a classifier by minimizing the classification error rate along the training samples. The experimental results were given to show the validity of our proposed approaches.