A new recursive prediction error algorithm is derived for the training of feedforward layered neural networks. The algorithm enables the weights in each neuron of the network to be updated in an efficient parallel manner and has better convergence properties than the classical back propagation algorithm. The relationship between this new parallel algorithm and other existing learning algorithms is discussed. Examples taken from the fields of communication channel equalization and nonlinear systems modelling are used to demonstrate the superior performance of the new algorithm compared with the back propagation routine.