  The semi-classical study of a 1-dimensional Schr\"odinger operator near a
non-degenerate maximum of the potential has lead Colin de Verdi\`ere and
Parisse to prove a microlocal normal form theorem for any 1-dimensional
pseudo-differential operator with the same kind of singularity. We present here
a generalization of this result to pseudo-differential integrable systems of
any finite degree of freedom with a Morse singularity. Our results are based
upon Eliasson's study of critical integrable systems.
