  We present a general method to account for full colour dependence Yang-Mills
amplitudes at loop level. The method fits most naturally into the framework of
multi-loop integrand reduction and in a nutshell amounts to consistently
retaining the colour structures of the unitarity cuts from which the integrand
is gradually constructed. This technique has already been used in the recent
calculation of the two-loop five-gluon amplitude in pure Yang-Mills theory with
all positive helicities, arXiv:1507.08797. In this note, we give a careful
exposition of the method and discuss its connection to loop-level Kleiss-Kuijf
relations. We also explore its implications for cancellation of nontrivial
symmetry factors at two loops. As an example of its generality, we show how it
applies to the three-loop case in supersymmetric Yang-Mills case.
