  We describe the decomposition of one-loop QCD amplitudes in terms of
colour-ordered building blocks. We give new expressions for the coefficients of
QCD colour structures in terms of ordered objects called primitive amplitudes,
for processes with up to seven partons. These results are needed in
computations of high-multiplicity scattering cross sections in
next-to-leading-order (NLO) QCD. We explain the origin of new relations between
multi-quark primitive amplitudes which can be used to optimise efficiency of
NLO computations. As a first application we compute the full-colour virtual
contribution to the cross section for W+4-jet production at the Large Hadron
Collider, and verify that it is very well approximated by keeping only the
leading terms in an expansion around the formal limit of a large number of
colours.
