The Self-organizing map (SOM) is an unsupervised learning method based on the neural computation, which has found wide applications. However, the learning process sometime takes multi-stable states, within which the map is trapped to an undesirable disordered state including topological defects on the map. These topological defects critically aggravate the performance of the SOM. In order to overcome this problem, we propose to introduce an asymmetric neighborhood function for the SOM algorithm. Compared with the conventional symmetric one, the asymmetric neighborhood function accelerates the ordering process even in the presence of the defect. However, this asymmetry tends to generate a distorted map. This can be suppressed by an improved method of the asymmetric neighborhood function. In the case of one-dimensional SOM, it is found that the required steps for perfect ordering is numerically shown to be reduced from O(N(3)) to O(N(2)). We also discuss the ordering process of a twisted state in two-dimensional SOM, which can not be rectified by the ordinary symmetric neighborhood function.