  We suggest the fermion doubling for all quarks and leptons. It is a
generalization of the neutrino doubling of the seesaw mechanism. The new quarks
and leptons are $SU(2)$ singlets and carry the electromagnetic charges of their
lighter counterparts. An $SU(3)$ {\it anomaly free global symmetry} or a
discrete symmetry can be introduced to restrict the Yukawa couplings. The form
of mass matrix is belonging to that of Nelson and Barr even though our model
does not belong to Barr's criterion. The weak CP violation of the
Kobayashi-Maskawa form is obtained through the spontaneous breaking of CP
symmetry at high energy scale. The strong CP solution is through a specific
form of the mass matrix. At low energy, the particle content is the same as in
the standard model. For a model with a global symmetry, in addition there
exists a massless majoron.
