A generalized branch and bound decision tree classifier is proposed which approximates the function of a full-search strategy when the training sample is sufficiently large to reflect the true data distribution. The classifier is an m-ary decision tree with each node representing a set of disjoint pattern classes. Associated with each set is a subspace of the feature space and a function estimating the maximum likelihood of any given feature vector x found in the subspace belonging to a pattern class of the set. By comparing the best-so-far likelihood of x belonging to any of the pattern classes already visited with such an estimate, one can decide if the corresponding node is worth visiting.