  The Lorentz invariant $CPT$ violation by using non-local interactions is
naturally incorporated in the Higgs coupling to neutrinos in the Standard
Model, without spoiling the basic $SU(2)_{L}\times U(1)$ gauge symmetry. The
neutrino--antineutrino mass splitting is thus realized by the mechanism which
was proposed recently, assuming the neutrino masses to be predominantly
Dirac-type in the Standard Model.
