  In a previous communication by two of us, Phys. Rev. Lett. 81, 1373 (1998),
the gauge-dependent deviations of the on-shell mass and total decay width from
their gauge-independent pole counterparts were investigated at leading order
for the Higgs boson of the Standard Model. In the case of the widths, the
deviation was found to diverge at unphysical thresholds, m_H = 2 root{xi_V} m_V
(V = W,Z), in the R_xi gauge. In this Brief Report, we demonstrate that these
unphysical threshold singularities are properly eliminated if a recently
proposed definition of wave-function renormalization for unstable particles is
invoked.
