The Sensitivity-Based Linear Learning Method (SBLLM) is a learning method for two-layer feedforward neural networks, based on sensitivity analysis, that calculates the weights by solving a system of linear equations. Therefore, there is an important saving in computational time which significantly enhances the behavior of this method compared to other learning algorithms. This paper introduces a generalization of the SBLLM by adding a regularization term in the cost function. The theoretical basis for the method is given and its performance is illustrated.