The paper considers a novel approach to learning the weight matrix of a fuzzy cognitive map. An overview of the state-of-the-art learning methods is presented with a specific emphasis on methods initially developed for artificial neural networks, and later adapted for FCMs. These have mostly been based on the concept of Hebbian learning. Inspired by the amount of success these methods have faced in the past, the paper proposes a new approach based on the application of the delta rule and the principle of backpropagation, both of which were originally designed for artificial neural networks as well. It is shown by simulation experiments and comparison with the existing approach based on nonlinear Hebbian learning that the proposed approach achieves favourable results, and that these are superior to those of the existing method by several orders of magnitude. Finally, some possible lines of further investigation are suggested.