Tests for break points detection in the law of random vectors have been proposed in several papers. Nevertheless, they have often little powers for alternatives involving a change in the dependence between components of vectors. Specific tests for detection of a change in the copula of random vectors have been proposed in recent papers, but they do not allow to conclude of a change in the dependence structure without condition that the margins are constant. The goal of this article is to propose a test for detection of a break in the copula when a change in marginal distribution occurs at a known instant. The performances of this test are illustrated by Monte Carlo simulations.