  SrIrO$_3$ crystallizes in a monoclinic structure of distorted hexagonal
perovskite at ambient pressure. The transport measurements show that the
monoclinic SrIrO$_3$ is a low-carrier density semimetal, as in the orthorhombic
perovskite polymorph. The electronic structure calculation indicates a
semimetallic band structure with Dirac bands at two high-symmetry points of
Brillouin zone only when spin-orbit coupling is incorporated, suggesting that
the semimetallic state is produced by the strong spin-orbit coupling. We argue
that the Dirac bands are protected by the non-symmorphic symmetry of lattice.
