Acupuncture points have been found in low electrical resistance areas compared to the surrounding tissue. The significance and details of the singular electrical properties of the acupuncture points are not clear at present. In most published studies about the electrical properties of the skin, there have been several problems related to measuring skin impedance. More careful consideration of the electrical properties of the skin and reliable measurements are needed. In this report, in order to improve the reliability of the measurements and clarify the electrical properties of the skin around the acupuncture points, we examined the existence of some parameters of the circular arc law that are little affected by the electrode area. Additionally, we performed multiple and simultaneous measurements of the skin impedance locus around the acupuncture points using the new method we propose. For evaluating the differences in electrical properties of the skin, we estimated the parameters of the circular arc law. As a result, we found that the parameters of the circular arc law (τ_m, β) are little affected by the electrode area. We also found that the differences of detailed electrical properties of the skin between acupuncture point and non-acupuncture point could be evaluated quantitatively by the parameters of the circular arc law, Z₀ and τ_m. These results suggest that the parameters of the circular arc law, τ_m, are useful in determining the location of the acupuncture points.