  One-loop amplitudes of gluons in N=4 gauge theory can be written as linear
combinations of known scalar box integrals with coefficients that are rational
functions. In this paper we show how to use generalized unitarity to basically
read off the coefficients. The generalized unitarity cuts we use are quadruple
cuts. These can be directly applied to the computation of four-mass scalar
integral coefficients, and we explicitly present results in next-to-next-to-MHV
amplitudes. For scalar box functions with at least one massless external leg we
show that by doing the computation in signature (--++) the coefficients can
also be obtained from quadruple cuts, which are not useful in Minkowski
signature. As examples, we reproduce the coefficients of some one-, two-, and
three-mass scalar box integrals of the seven-gluon next-to-MHV amplitude, and
we compute several classes of three-mass and two-mass-hard coefficients of
next-to-MHV amplitudes to all multiplicities.
