Sensitivity is initially investigated for the construction of a network prior to its design. Sensitivity analysis applied to network pruning seems particularly useful and valuable when network training involves a large amount of redundant data. This paper proposes a novel learning algorithm for the construction of radial basis function (RBF) classifiers using sensitive vectors (SenV), to which the output is the most sensitive. In training, the number of hidden neurons and the centers of their radial basis functions are determined by the maximization of the output's sensitivity to the training data. In classification, the minimal number of such hidden neurons with the maximal sensitivity is the most generalizable to unknown data. Our experimental results suggest that our proposed methodology outperforms classical RBF classifiers constructed by clustering.