  We calculate the one-loop QCD corrections for the decay of an off-shell
vector boson with vector couplings into two pairs of quarks of equal or unequal
flavours keeping all orders in the number of colours. These matrix elements are
relevant for the calculation of the next-to-leading order ${\cal
O}(\alpha_s^3)$ 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.
We use standard techniques for computing the interference of one-loop and tree
level Feynman diagrams, but organise the results in terms of combinations of
scalar loop integrals that are finite in the limit of vanishing Gram
determinants and are therefore numerically stable.
