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Melanoma diagnosis depends on the experience of doctors. Symmetry is one of the most important factors to measure, since asymmetry shows an uncontrolled growth of cells, leading to melanoma cancer. A system for melanoma detection in diagnosing melanocytic diseases with high sensitivity is proposed here. Two different sets of features are extracted based on the importance of the ABCD rule and symmetry evaluation to develop a new architecture. Support Vector Machines are used to classify the extracted sets by using both an alternative labeling method and a structure divided into two different classifiers which prioritize sensitivity. Although feature extraction is based on former works, the novelty lies in the importance given to symmetry and the proposed architecture, which combines two different feature sets to obtain a high sensitivity, prioritizing the medical aspect of diagnosis. In particular, a database provided by Hospital Universitario de Gran Canaria Doctor Negrín was tested, obtaining a sensitivity of 100% and a specificity of 66.66% using a leave-one-out validation method. These results show that 66.66% of biopsies would be avoided if this system is applied to lesions which are difficult to classify by doctors.