  We investigate Type II orientifolds on non-factorizable torus with and
without its oribifolding. We explicitly calculate the Ramond-Ramond tadpole
from string one-loop amplitudes, and confirm that the consistent number of
orientifold planes is directly derived from the Lefschetz fixed point theorem.
We furthermore classify orientifolds on non-factorizable Z_N x Z_M orbifolds,
and construct new supersymmetric Type IIA orientifold models on them.
