We study the behavior of bivariate empirical copula process 𝔾 n (·, ·) 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 𝔾 n (·, ·) by a Gaussian process when k n /n↘γ as n → ∞, where 0 ≤ γ ≤1.