  We strictly define two set Wave-function Renormalization Constants (WRC)
under the LSZ reduction formula for unstable particles at the first time. Then
by introducing antiparticle's WRC and the CPT conservation law we obtain a new
wave-function renormalization condition which can be used to totally determine
the two set WRC. We calculate two physical processes to manifest the
consistence of the present wave-function renormalization prescription with the
gauge theory in standard model. We also prove that the conventional
wave-function renormalization prescription which discards the imaginary part of
unstable particle's WRC leads to physical amplitude gauge dependent.
