  We show that in a Complementary two-Higgs doublet model(C2HDM) the CP
violating phase in the CKM matrix can be generated spontaneously, dangerous
FCNC can be naturally suppressed and the strong CP problem can also be avoided.
The two Higgs doublets in the model are complementary in the sense that none of
them is enough to describe masses of a given type of quarks. We find that the
strength of FCNC is suppressed by the strength of Yukawa couplings of the first
generation quark and the tree-level FCNC is sufficiently small. Using an
explicit example, we show that radiative correction to the assumed Yukawa
couplings can modify the discussion about the strong $\theta$. The correction
to the strong $\theta$ is estimated to be less than around
$10^{-12}\sim10^{-10}$ which can be tested in future experiment.
