The author considers the algebra \({\mathcal G}(\mathbb{R}^m)\) of Colombeau generalized function [J. F. Colombeau, “New generalized functions and multiplication of distributions”, North Holland Math. Stud. 84, Amsterdam (1984; Zbl 0532.46019)] which is a differential \(\mathbb{C}\)-algebra containing a copy of the space \({\mathcal D}'(\mathbb{R}^m)\) of Schwartz distributions. In this paper the author proves the following theorem. Let \(N_0\) denote the set of all natural numbers. For each \(p\in N^m_0\) let \(\widetilde\delta^p_0\) and \(\widetilde x^p_+\) denote the imbeddings in \({\mathcal G}(\mathbb{R}^m)\) of the distribution \(\delta^p(x)\) (the \(p\)th derivative of the Dirac \(\delta\)) and the function \(x^p_+\) given by \[ x^p_+= \begin{cases} x^p &\text{for }x\geq 0\\ 0 &\text{for }x< 0\end{cases} \] then their product in this algebra admits an associated distribution which can be computed as \({(-1)^{|p|} p!\over 2^m}\delta(x)\). Some natural corollaries are also deduced.