  We propose a Z$_2$ index theorem for a generic topological superconductor in
class D. Introducing a particle-hole symmetry breaking term depending on a
parameter and regarding it as a coordinate of an extra dimension, we define the
index of the zero modes and corresponding topological invariant for such an
extended Hamiltonian. It is shown that these are related with the number of the
zero modes of the original Hamiltonian modulo two.
