In this paper we develope a hybrid learning rule to improve the robustness of multi-layer Perceptions. In most neural networks the activation of a neuron is deternined by a nonlinear transformation of the weighted sum of inputs to the neurons. Investigating the behaviour of activations of hidden layer neurons a new learning algorithm is developed for improved robustness for multi-layer Perceptrons. Unlike other methods which reduce the network complexity by putting restrictions on synaptic weights our method based on error-backpropagation increases the complexity of the underlying proplem by imposing it saturation requirement on hidden layer neurons. We also found that the additional gradient-descent term for the requirement corresponds to the Hebbian rule and our algorithm incorporates the Hebbian learning rule into the error back-propagation rule. Computer simulation demonstrates fast learning convergence as well as improved robustness for classification and hetero-association of patterns.