  In a general two-Higgs-doublet model (2HDM), without the {\it ad hoc}
discrete symmetries to prevent tree-level flavor-changing-neutral currents, an
extra phase angle in the charged-Higgs-fermion coupling is allowed. We show
that the charged-Higgs amplitude interferes destructively or constructively
with the standard model amplitude depending crucially on this phase angle. The
popular model I and II are special cases of our analysis. As a result of this
phase angle the severe constraint on the charged-Higgs boson mass imposed by
the inclusive rate of $b\to s\gamma$ from CLEO can be relaxed. We also examine
the effects of this phase angle on the neutron electric dipole moment.
Furthermore, we also discuss other constraints on the charged-Higgs-fermion
couplings coming from measurements of $B^0-\bar{B^0}$ mixing, $\rho_0$, and
$R_b$.
