  The number of tree-rooted maps, that is, rooted planar maps with a
distinguished spanning tree, of size $n$ is C(n)C(n+1) where
C(n)=binomial(2n,n)/(n+1) is the nth Catalan number. We present a (long
awaited) simple bijection which explains this result. We prove that our
bijection is isomorphic to a former recursive construction on shuffles of
parenthesis systems due to Cori, Dulucq and Viennot.
