  We calculate the three- and four-loop corrections to the massless fermion
propagator in three-dimensional quenched Quantum Electrodynamics with
four-component fermions. The three-loop correction is finite and gauge
invariant but the four-loop one has singularities except in the Feynman gauge
where it is also finite. Our results explicitly show that, up to four loops,
gauge-dependent terms are completely determined by lower order ones in
agreement with the Landau-Khalatnikov-Fradkin transformation.
