When applying the SOM neural network for the identification problem in general, and character recognition problem in particular, the authors found that SOM neural network offers prospects of this problem. However, for each type of input data, weight structure and function that assess the dissimilarity should be adapted to make the network operate more efficiently. In this paper, the authors propose a new weighting structure for SOM neural network to present the shape characteristics of the object. Then, the article develop a new distance function that is used to assess the non-similarity of the characteristics and applications for character recognition problem. The experimental results show that the improved solution makes the SOM neural network capable of better character recognition.