Radial Basis Function (RBF) Network is popularly used for solving pattern recognition problems. The training of RBF Network is faster compared to multi layer perceptron using error backpropagation. However, the RBF Network uses the pseudo inverse matrix to calculate weights from the hidden layer to the output layer. Thus calculation cost increases when the number of data and the number of hidden units increase. In addition, in RBF Network the decision of optimum number of hidden units is difficult. It is also more prone to overtraining, needing repeated train and test cycles to ascertain a proper number of the Network hidden units, so that generalization performance is good. In this work, we propose a technique to set up RBF network parameters which is fast, as well as the number of hidden units are automatically determined. We start with training a Self-Organizing Maps (SOM), which is a unsupervised training, though our samples are labeled. SOM can find the distribution of data in multidimensional space, and map it on a two dimensional display. The results of SOM network is used to calculate the RBF parameters. It is shown by experiments that using the proposed method, RBF network parameters can be determined much faster compared to existing technique. Moreover, the recognition rate for the test data was higher, showing better generalization performance.