  We construct a gauge invariant regularisation scheme for pure SU(N)
Yang-Mills theory in fixed dimension four or less (for N = infinity in all
dimensions), with a physical cutoff scale Lambda, by using covariant higher
derivatives and spontaneously broken SU(N|N) supergauge invariance. Providing
their powers are within certain ranges, the covariant higher derivatives cure
the superficial divergence of all but a set of one-loop graphs. The finiteness
of these latter graphs is ensured by properties of the supergroup and gauge
invariance. In the limit Lambda tends to infinity, all the regulator fields
decouple and unitarity is recovered in the renormalized pure SU(N) Yang-Mills
theory. By demonstrating these properties, we prove that the regularisation
works to all orders in perturbation theory.
