Recently, Artificial Neural Networks (ANNs) have become popular because they can learn complex mappings from the input/output data and are relatively easy to implement in any application. Although, a disadvantageous aspect of their usage is that they need (usually a significant amount of) time to be trained, which scales with the structural parameters of the networks and with the quantity of the input data. However, the training can be done offline; it has a non-negligible cost and further, can cause a delay in the operation. Fuzzy Neural Networks (FNNs) are the combinations of ANNs and fuzzy logic in order to incorporate the advantages of both methods (the learning ability of ANNs and the thinking ability of fuzzy logic). FNNs have fuzzy values in their weight parameters and in the output of each neuron. Circular Fuzzy Neural Networks (CFNNs) are FNNs with their topology realigned to a circular topology and the connections between the input layer and hidden layer trimmed. This may result in a dramatic reduction in the training time, while the precision and accuracy of the network are not affected. To further increase the speed of the training of the ANNs, FNNs, or CFNNs used for classification, a new training procedure is introduced in this paper: instead of directly using the training data in the training phase, the data is first clustered and the neural networks are trained by using only the centers of the obtained clusters.