The Self Organizing Map (SOM) model is an unsupervised learning neural network that has been successfully applied as a data mining tool. The advantages of the SOMs are that they preserve the topology of the data space, they project high dimensional data to a lower dimension representation scheme, and are able to find similarities in the data. However, the learning algorithm of the SOM is sensitive to the presence of noise and outliers as we will show in this paper. Due to the influence of the outliers in the learning process, some neurons (prototypes) of the ordered map get located far from the majority of data, and therefore, the network will not effectively represent the topological structure of the data under study. In this paper, we propose a variant to the learning algorithm that is robust under the presence of outliers in the data by being resistant to these deviations. We call this algorithm Robust SOM (RSOM). We will illustrate our technique on synthetic and real data sets.