An derivation method of a nail apparatus melanoma discrimination threshold includes a first step of assuming a color image of longitudinal melanonychia as three-dimensional vectors each composed of RGB parameter values of each pixel and finding an angle between each of the three-dimensional vectors and a reference vector, a second step of finding a probability of occurrence according to a frequency distribution of the angles found in the first step, and a third step of finding, according to the probability of occurrence found in the second step, a threshold for a parameter to discriminate whether the longitudinal melanonychia is malignant or benign.