Abstract
We characterize the transformation, defined for every copula $C$ by $C_h(x,y):=h^{[-1]}\lp C(h(x),h(y))\rp$, where $x$ and $y$ belong to $\lsp 0,1 \rsp$ and $h$ is
a strictly increasing and continuous function on $\lsp 0,1 \rsp$. We study this transformation
also in the class of quasi--copulas and semicopulas.