Let $F_p^n (x)$ be an $(n,p)$–binomial distribution function and be the set of all infinitely divisible laws. We define \[ \rho \left( {F_p^n ,\mathfrak{G}} \right) = \mathop {\inf }\limits_{G \in \mathfrak{G}} \mathop {\sup }\limits_x \left| {F_p^n (x) - G(x)} \right|. \]Then, \[ \mathop {\sup }\limits_{0 \leqq p \leqq 1} \rho \left( {F_p^n ,\mathfrak{G}} \right) < \frac{{C_0 }} {{\sqrt n }}, \] where $C_0 $ is an absolute constant.