  At one loop in the conventional on-mass-shell renormalization scheme, the
production and decay rates of the Higgs boson H exhibit singularities
proportional to (2 M_V - M)^{-1/2} as the Higgs-boson mass M approaches from
below the pair-production threshold of a vector boson V with mass M_V. This
problem is of phenomenological interest because the values 2 M_W and 2 M_Z,
corresponding to the W- and Z-boson thresholds, lie within the M range
presently favoured by electroweak precision data. We demonstrate how these
threshold singularities are eliminated when the definitions of mass and total
decay width of the Higgs boson are based on the complex-valued pole of its
propagator. We illustrate the phenomenological implications of this
modification for the partial width of the H -> W^+ W^- decay.
