  We study a complex action theory (CAT) whose path runs over not only past but
also future. We show that if we regard a matrix element defined in terms of the
future state at time $T_B$ and the past state at time $T_A$ as an expectation
value in the CAT, then we are allowed to have the Heisenberg equation, the
Ehrenfest's theorem and the conserved probability current density. In addition
we show that the expectation value at the present time $t$ of a future-included
theory for large $T_B-t$ and large $t- T_A$ corresponds to that of a
future-not-included theory with a proper inner product for large $t- T_A$.
Hence the CAT with future explicitly present in the formalism and influencing
in principle the past is not excluded phenomenologically, because the effects
are argued to be very small in the present era. Furthermore we explicitly
derive the Schr\"{o}dinger equation and Hamiltonian for the future state via
path integral, and confirm that the Hamiltonian is given by the Hermitian
conjugate of the Hamiltonian for the past state.
