  In this manuscript, a way solves the FCNC problem in 2HDM radically and leads
to CP violation explicitly is demonstrated. The derivation starts from a most
general $3 \times 3$ mass matrix $M$ containing eighteen parameters, which
applies to all fermion types, and then reduces the number of parameters down to
five with a Hermitian condition modified in this manuscript between the real
part and imaginary part of $M$. All matrix pairs thus derived will be
diagonalized simultaneously by a same $U$ matrix which means FCNCs won't appear
at tree-level anymore. Subsequently, an assumption of $A=A_1=A_2=A_3$ is
imposed and four special solutions are thus found which reveal $S_3$ and $S_2$
symmetries among fermion generations respectively. Consequently, as a
by-product of solving the FCNC problem, complex CKM matrices appear if the
symmetries were assigned to up- and down-type quarks suitably. Unfortunately,
CKM elements thus derived are very different to the experimentally detected
values. The CP strength of this model, estimated by the Jarlskog invariant, is
four orders higher than the one predicted by the standard model. This
difference is in fact reasonable since we don't see any such symmetries in our
present universe. However, if they had appeared in some early stages of our
universe, such a strong CP strength may provide a way to account for at least
part of the discrepancy between the observed BAU and that predicted by the
standard model.
