  New copulas, based on perturbation theory, are introduced to clarify a
\emph{symmetrization} procedure for asymmetric copulas. We give also some
properties of the \emph{symmetrized} copula. Finally, we examine families of
copulas with a prescribed symmetrized one. By the way, we study topologically,
the set of all symmetric copulas and give some of its classical and new
properties.
