The error probability of the partitioning classification rule is shown to converge to the Bayes error faster than 1/n under certain conditions. The resubstitution and the deleted error estimates for the partitioning classification rule from a sample (X 1 ,Y 1 ),...,(X n ,Y n ) are studied. The random part of the resubstitution estimate is shown to be small for arbitrary partition and for any distribution of (X,Y). If we assume that X has a density f and the partitions consist of rectangles, then the difference between the expected value of the estimate and the Bayes error restricted to the partition is less than a constant times 1/n. The main result of the paper is that, under the same conditions, for both estimates the difference between the estimate and the real error probability of the classification rule is asymptotically normal with 0 mean and variance L * /2, where L * is the Bayes error.