Abstract : The concept of copula is a useful tool to model multivariate distributions but the construction of tail dependent high dimensional copulas remains a challenging problem. We propose a new copula constructed by introducing a latent factor. Conditional independence with respect to this factor and the use of a nonparametric class of bivariate copulas lead to interesting properties like explicitness, flexibility and parsimony. We propose a pairwise moment-based inference procedure and prove asymptotic normality of our estimator. Finally we illustrate our model on simulated and real data.