In the paper [1], it was given a function which belongs to the bounded Stummel modulus classes but not in Stummel classes. The given proof of this function properties in that paper was not obvious and very concise. By using the countable linearity property of integral, polar coordinate of integration, other properties of Lebesgue measure and integration, and some observation on the geometric property of the open ball in Euclidean spaces, we prove in detail the properties of this function.