  Despite its simplicity, the unitary gauge is not a popular choice for
practical loop calculations in gauge theories, due to the lack of off-shell
renormalizability. We study the renormalization properties of the off-shell
Green functions of the elementary electron fields in the massive QED, in order
to elucidate the origin and structure of the extra ultraviolet divergences
which exist only in the unitary gauge. We find that all these divergences
affect the Green functions in a trivial way such that in coordinate space the
off-shell Green functions are in fact multiplicatively renormalizable. This
result may generalize to the abelian and non-abelian Higgs theories, for which
the unitary gauge might bring much simplification to the loop calculations.
