  let f be an endomorphism of a complex projective space, of degree bigger than
one. Let us call an algebraic subset exceptional for f, if its inverse image is
set-theoretically equal to itself. J.-Y. Briend, S. Cantat and M. Shishikura
proved that an irreducible set like this is a linear subspace. In this paper,
we obtain a bound for the number of codimension-two exceptional subspaces. In
particular, we show that an endomorphism of the projective plane can be
completely ramified at nine points at most.
