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_#epsilon#-gauges including 't Hooft-Feynman gauge but excluding Landau gauge. In this paper we construct a new renormalization scheme in which the multiplicative radiative modification factor, C"a_m_o_d, is equal to unity for all R_#epsilon#-gauges, including both 't Hooft-Feynman and Landau gauges. This scheme makes C"a_m_o_d equal to unity by specifying a convenient subtraction co...