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Prompt diagnosis is the most reliable solution for an effective treatment of melanoma. There is an ongoing research for providing computer-aided imaging tools in order to support the early detection and diagnosis of malignant melanomas. The first step towards producing such a diagnosis system is the automated and accurate boundary detection of skin lesion. Therefore, the present study introduces a new, simple, and very fast algorithm that has the ability to detect effectively and automatically the border of potential melanoma. The complexity of the proposed algorithm is O(√N), and thus the execution time, is dramatically minimized.