We investigate the properties of a dressed electron which reduces, in
a particular class of gauges, to the usual fermion. A one-loop calcula
tion:of the propagator is presented. We show explicitly that an infrar
ed finite, multiplicative, mass shell renormalization is possible for
this dressed electron, or, equivalently, for the usual fermion in the
above-mentioned gauges. The results are in complete accord with previo
us conjectures.