  We consider the $c=1$ matrix model deformed by the operator ${1\over 2}
M\Tr\Phi^{-2}$, which was conjectured by Jevicki and Yoneya to describe a
two-dimensional black hole of mass $M$. We calculate the exact non-perturbative
$S$-matrix and show that all the amplitudes involving an odd number of
particles vanish at least to all orders of perturbation theory. We conjecture
that these amplitudes vanish non-perturbatively and prove this for the $2n \to
1$ scattering. For the 2-- and 4--particle amplitudes we give some leading
terms of the perturbative expansion.
