Self-organizing maps (SOMs) are aimed to learn a representation of the input distribution which faithfully describes the topological relations among the clusters of the distribution. For some data sets and applications, it is known beforehand that some regions of the input space cannot contain any samples. Those are known as forbidden regions. In these cases, any prototype which lies in a forbidden region is meaningless. However, previous self-organizing models do not address this problem. In this paper, we propose a new SOM model which is guaranteed to keep all prototypes out of a set of prespecified forbidden regions. Experimental results are reported, which show that our proposal outperforms the SOM both in terms of vector quantization error and quality of the learned topological maps.