Many applications require classification of examples into one of several classes. A common way of designing such classifiers is to determine the class based on the outputs of several binary classifiers. We consider some of the most popular methods for combining the decisions of the binary classifiers, and improve existing bounds on the error rates of the combined classifier over the training set. We also describe a new method for combining binary classifiers. The method is based on stacking a neural network and, when used with support vector machines as the binary learners, substantially decreased the error rate in two vowel classification tasks.