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This paper proposes a framework for constructing and training a radial basis function (RBF) neural network. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit and also to detect and remove inactive units. The structure of the Gaussian functions is modi"ed using a pseudoGaussian function (PG) in which two scaling parameters are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater #exibility with respect to function approximation. Other important characteristics of the proposed neural system are that the activation of the hidden neurons is normalized which, as described in the bibliography, provides a better performance than nonnormalization and instead of using a single parameter for the output weights, these are functions of the input variables which leads to a signi"cant reduction in the number of hidden units compared to the classical RBF network. Finally, we examine the result of applying the proposed algorithm to time series prediction.