The problem of smoothness of adaptive meshes produced by the Self-Organizing Maps is considered. It is shown that to improve the mesh smoothness, it is necessary to increase the learning radius. This leads, in turn, to the border effect. The main goal of this paper is to develop a technique allowing us to use a large learning radius for obtaining the sufficiently smooth adaptive meshes without border effect. The technique does not require changing the structure of the SOM neuron layer, and affects only the way of the SOM learning. In addition, an inherent parallelism of the SOM neural network is preserved in the proposed learning algorithm and the algorithm is simple to implement.