Copulas were introduced as a method for modeling the dependence structure between random variables and for constructing a multivariate distribution function from its marginals. Many copulas were introduced in the literature to suit different models having different properties. Among which is the Cuadras copula introduced by Cuadras [3]. A drawback of the Cuadras copula is the limited range of dependence structure that it allows for modeling random variables. In this paper, we propose a new extension of the Cuadras copula that permits a wider range of dependence between the involved random variables, thus opening the way for an increased number of applications. Properties of the new extended copula with an example illustrating our findings will be given.