In the last decade we can observe increasing number of applications based on the Artificial Intelligence that are designed to solve problems from different areas of human activity. The reason why there is so much interest in these technologies is that the classical way of solutions does not exist or these technologies are not suitable because of their robustness. They are often used in applications like Business Intelligence that enable to obtain useful information for high-quality decision-making and to increase competitive advantage.One of the most widespread tools for the Artificial Intelligence are the artificial neural networks. Their high advantage is relative simplicity and the possibility of self-learning based on set of pattern situations.For the learning phase is the most commonly used algorithm back-propagation error (BPE). The base of BPE is the method minima of error function representing the sum of squared errors on outputs of neural net, for all patterns of the learning set. However, while performing BPE and in the first usage, we can find out that it is necessary to complete the handling of the learning factor by suitable method. The stability of the learning process and the rate of convergence depend on the selected method. In the article there are derived two functions: one function for the learning process management by the relative great error function value and the second function when the value of error function approximates to global minimum.The aim of the article is to introduce the BPE algorithm in compact matrix form for multilayer neural networks, the derivation of the learning factor handling method and the presentation of the results.