  The electroweak equivalence theorem quantitatively connects the physical
amplitudes of longitudinal massive gauge bosons to those of the corresponding
``unphysical'' would-be Goldstone bosons. Its precise form depends on both the
gauge fixing condition and the renormalization scheme. Our previous
modification-free schemes have applied to a broad class of $R_\xi$ gauges
including 't Hooft-Feynman gauge but excluding Landau gauge. In this paper we
construct a new renormalization scheme in which the radiative modification
factor, $C_{mod}^a$, is equal to unity for all $R_\xi$-gauges, including both
't Hooft-Feynman and Landau gauges. This scheme makes $C_{mod}^a$ equal to
unity by specifying a convenient subtraction condition for the would-be
Goldstone boson wavefunction renormalization constant $Z_{\phi^a}$. We build
the new scheme for both the standard model and the effective Lagrangian
formulated electroweak theories (with either linearly or non-linearly realized
symmetry breaking sector). Based upon these, a new prescription, called
``divided equivalence theorem'', is further proposed for extending the high
energy region applicable to the equivalence theorem.
