  We investigate the relation between the $S$-matrix unitarity
($SS^{\dagger}=1$) and the renormalizability, in theories with negative norm
states. The relation has been confirmed in many theories, such as gauge
theories, Einstein gravity and Lifshitz-type non-relativistic theories by
analyzing the unitarity bound, which follows from the $S$-matrix unitarity and
the norm positivity. On the other hand, renormalizable theories with a higher
derivative kinetic term do not necessarily satisfy the unitarity bound
essentially because the unitarity bound does not hold due to the negative norm
states. In these theories, it is not clear if the $S$-matrix unitarity provides
a nontrivial constraint related to the renormalizability. In this paper we
introduce scalar field models with a higher derivative kinetic term and analyze
the $S$-matrix unitarity. We have positive results of the relation.
