  In the framework of nonstandard analysis, Bang-He Li and the author defined
the product of any two distributions on $R^n$ via their harmonic
representations. The product of $\delta (x_{1},..., x_{n})$ and $\delta
(x_{1})$ was calculated by Kuribayashi and the author in [LK]. In this paper,
the result of [LK] is improved to $$\delta (x_{1},..., x_{n})\circ \delta
(x_{1}) =\dfrac{1}{2\pi\rho} \delta (x_{1},..., x_{n}) {mod} {infinitesimals}$$
where $\rho$ is a positive infinitesimal. Moreover two combinatorial identities
are obtained as byproducts.
