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There is an ongoing research effort to provide computer-aided imaging tools in order to support the diagnosis and early detection of malignant melanomas. The first step towards producing such a 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 possible melanoma. The complexity of the proposed algorithm is O(√N) and thus the execution time is dramatically minimized.