In this paper, the dynamic security of a large power system against any critical contingency is predicted by a new type of radial basis function neural network, RBF-R NN, as it classifies the system's transient stability status online. In order to keep the number of measurements limited, as well as to reduce the complexity of the NNs used, the minimum redundancy maximum relevance is adopted as a feature selection method. Moreover, the classification performance of the RBF-R NNs is improved by eliminating the training set instances that are close to the security boundary. The proposed method is applied on a 16-generator-68-bus test system and the performance of the adopted RBF-R NNs is compared with RBF NNs, as well as with multilayer perceptrons. The simulation results show that a significant improvement in prediction accuracy is obtained by the RBF-R NNs together with the feature selection and the elimination of boundary instances.