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A new learning algorithm based on L2-norm approximation to define the relationship between two neurons in a recurrent neural network is proposed in this paper. The learning process utilizes the statistical relationship between each component of the input pattern with respect to every other component. The activation function of a neuron is a rectangular function whose position changes adaptively with respect to the input pattern and its left and right wings are decided by the mean of maximum variations of the training signals to that neuron. The new training algorithm is applied for recognition of faces images with varying expressions. 975 face images of 13 persons from the Carnegie Mellon University (CMU) face expression variant database are used for evaluating the performance of the network. The network has been trained with 5 images and tested with the remaining 70 images of each person. The recurrent neural network with the new learning algorithm recognized all the 13 persons in this database without error.