AbstractWith regard to competitive learning a neural network model consisting of two layers of neurons was constructed and a new energy (loss) function to ensure that the network will converge uniquely to the desired state is proposed. It was proved that when the number of cells in the hidden layer is equal to the number of the input patterns, this model does not have any local minima of the energy function other than the one that yields the global minimum and, consequently, converges to the global minimum from any initial values of the synaptic connections.In this equilibrium the network is organized to the state where only a single hidden cell responds to its corresponding input pattern. This model is compared with the other models of competitive learning proposed up to the present. Then a model of the associative memory based on this competitive learning model is proposed. In this model of the associative memory only output patterns that are presented during the learning are recalled even in response to an input that has never been presented during the learning. This model has an extra advantage in that the input patterns are requested to be neither orthogonal nor independent of each other.