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Skin lesion border irregularity is considered an important clinical feature for the early diagnosis of melanoma, representing the B feature in the ABCD rule. In this article we propose an automated approach for skin lesion border irregularity detection. The approach involves extracting the skin lesion from the image, detecting the skin lesion border, measuring the border irregularity, training a Convolutional Neural Network and Gaussian naive Bayes ensemble, to the automatic detection of border irregularity, which results in an objective decision on whether the skin lesion border is considered regular or irregular. The approach achieves outstanding results, obtaining an accuracy, sensitivity, specificity, and F-score of 93.6%, 100%, 92.5% and 96.1%, respectively.