  We obtain the matter-graviton scattering amplitude in the gravitational
theory of quadratic curvature, which has $R_{\mu\nu}^2$ term in the action.
Unitarity bound is not satisfied because of the existence of negative norm
states, while an analog of unitarity bound for $S$-matrix unitarity holds due
to the cancelation among the positive norm states and negative norm ones in the
unitarity summation in the optical theorem. The violation of unitarity bound is
a counter example of Llewellyn Smith's conjecture on the relation between
tree-level unitarity and renormalizability. We have recently proposed a new
conjecture that an analog of the unitarity bound for $S$-matrix unitarity gives
the equivalent conditions to those for renormalizability. We show that the
gravitational theory of quadratic curvature is a nontrivial example consistent
with our conjecture.
