A new algorithm is presented for Multi-Layer Perceptron Neural Networks training, which is called AR\(\gamma\)-GLE (Acelerador Regresivo versin \(\gamma\) con Gradiente Local de Error). This algorithm is based in the same principles that let parameter actualization in AR\(\gamma\) algorithm. This last one is an algorithm created in adaptive filtering context and is obtained from discretization of a continuous time algorithm based on the second derivative adjustment of the parameter estimate. AR\(\gamma\)-GLE algorithm is validated through different problems related to pattern recognition and fitting function. Results show both good convergence as generalization, overcomming in the experiments the inherent disadvantages of backpropagation algorithm (without a significant increase in the algorithm complexity) related to the unforseeable influence of the learnig rate.