Removal of cloud interference is a crucial step for the exploitation of the spectral information stored in optical satellite images. Several cloud masking approaches have been developed through time, based on direct interpretation of the spectral and temporal properties of clouds through thresholds. The problem has also been tackled by machine learning methods with artificial neural networks being among the most recent ones. Detection of bright non-cloud objects is one of the most difficult tasks in cloud masking applications since spectral information alone often proves inadequate for their separation from clouds. Scientific attention has recently been redrawn on self-organizing maps (SOMs) because of their unique ability to preserve topologic relations, added to the advantage of faster training time and more interpretative behavior compared to other types of artificial neural networks. This study evaluated a SOM for cloud masking Sentinel-2 images and proposed a fine-tuning methodology to separate clouds from bright land areas. The fine-tuning process which is based on the output of the non-fine-tuned network, at first directly locates the neurons that correspond to the misclassified pixels. Then, the incorrect labels of the neurons are altered without applying further training. The fine-tuning method follows a general procedure, thus its applicability is broad and not confined only in the field of cloud-masking. The network was trained on the largest publicly available spectral database for Sentinel-2 cloud masking applications and was tested on a truly independent database of Sentinel-2 cloud masks. It was evaluated both qualitatively and quantitatively with the interpretation of its behavior through multiple visualization techniques being a main part of the evaluation. It was shown that the fine-tuned SOM successfully recognized the bright non-cloud areas and outperformed the state-of-the-art algorithms: Sen2Cor and Fmask, as well as the version that was not fine-tuned.