Histopathological images are widely used to diagnose diseases such as skin cancer. As digital histopathological images are typically of very large size, in the order of several billion pixels, automated identification of abnormal cell nuclei and their distribution within multiple tissue sections would enable rapid comprehensive diagnostic assessment. In this paper, we propose a deep learning-based technique to segment the melanoma regions in Hematoxylin and Eosin-stained histopathological images. In this technique, the nuclei in an image are first segmented using a deep learning neural network. The segmented nuclei are then used to generate the melanoma region masks. Experimental results show that the proposed method can provide nuclei segmentation accuracy of around 90% and the melanoma region segmentation accuracy of around 98%. The proposed technique also has a low computational complexity.