Malignant melanoma is a popular cancer among youth; it is desirable to have a fast and convenience way to determine this disease in its early stage. One of the clinical features in diagnosis is related to the shape of lesions. In previous studies, circularity is commonly used as the asymmetric measurement of skin lesions. However, this measurement depends very much on the accuracy of the segmentation result. In this paper, we present an artificial neural network model to improve the measurements of the asymmetries of lesions that may have fuzzy borders. The main idea is enhancing the symmetric distant (eSD) with a number of variations. Results from experiments, which use the digitized images from the Lesion Clinic in Vancouver, Canada have shown the good discriminating power of the neural network model.