Backpropagation (BP) networks are a class of artificial neural network model that has been widely used in many areas of interest. One difficulty in adopting this model is the need to predetermine a suitable network size, particularly, the number of hidden nodes. A common approach is to start with an oversized network and then the size is reduced by eliminating unnecessary nodes and links. In this paper, starting from the viewpoint of pattern classification theory, a study on the characteristics of hidden nodes in oversized networks is reported. The study shows that four categories of excessive hidden nodes can be found in an oversized network. A new node pruning algorithm to attain appropriate size BP networks is then proposed by detecting and removing those excessive nodes. Moreover, the algorithm is extended to cater for the larger class of problems, i.e. real-to-real mapping. Unlike previous works, the concept of “excessiveness” advocated here has strong indications whether a node can be removed without impairing the performance of original network and hence the proposed algorithm is useful in obtaining a network that is optimized with both the network size and performance. The effectiveness of the proposed algorithm has been demonstrated through the N-bit parity problems and the experiment in predicting the chaotic time series.