  We compute the one-loop QCD amplitudes for the decay of an off-shell vector
boson with vector couplings into a quark-antiquark pair accompanied by two
gluons keeping, for the first time, all orders in the number of colours.
Together with previous work this completes the calculation of the necessary
one-loop amplitudes needed for the calculation of the next-to-leading order
O(alpha_s^3) corrections to four jet production in electron-positron
annihilation, the production of a gauge boson accompanied by two jets in
hadron-hadron collisions and three jet production in deep inelastic scattering.
