  We show that all multivariate Extreme Value distributions, which are the
possible weak limits of the $K$ largest order statistics of iid sequences, have
the same copula, the so called K-extremal copula. This copula is described
through exact expressions for its density and distribution functions. We also
study measures of dependence, we obtain a weak convergence result and we
propose a simulation algorithm for the K-extremal copula.
