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The process of removing occluding hair has a relevant role in the early and accurate diagnosis of skin cancer. It consists of detecting hairs and restore the texture below them, which is sporadically occluded. In this work, we present a model based on convolutional neural networks for hair removal in dermoscopic images. During the network's training, we use a combined loss function to improve the restoration ability of the proposed model. In order to train the CNN and to quantitatively validate their performance, we simulate the presence of skin hair in hairless images extracted from publicly known datasets such as the PH2, dermquest, dermis, EDRA2002, and the ISIC Data Archive. As far as we know, there is no other hair removal method based on deep learning. Thus, we compare our results with six state-of-the-art algorithms based on traditional computer vision techniques by means of similarity measures that compare the reference hairless image and the one with hair simulated. Finally, a statistical test is used to compare the methods. Both qualitative and quantitative results demonstrate the effectiveness of our network.