We find a (nonlocal) gauge where the wavefunction renormalization constant
does not get any corrections for all momenta in the hard-dense loop
approximation. In this gauge, we solve the Schwinger-Dyson equations for
the diquark condensate in dense QCD to calculate the Cooper pair gap. We
determine not only the exponent but also the prefactor of the gap in a
gauge independent way. We find that the higher order corrections increase
the gap only by about 1.6 times to the leading order gap at Coulomb gauge.