  We study the behavior of bivariate empirical copula process
$\mathbb{G}_n(\cdot,\cdot)$ on pavements $[0,k_n/n]^2$ of $[0,1]^2,$ where
$k_n$ is a sequence of positive constants fulfilling some conditions. We
provide a upper bound for the strong approximation of
$\mathbb{G}_n(\cdot,\cdot)$ by a Gaussian process when $k_n/n \searrow \gamma$
as $n\rightarrow \infty,$ where $0 \leq \gamma \leq 1.$
