  We propose a systematic way to carry out the method introduced in
hep-th/0410077 for computing certain unitarity cuts of one-loop N=4 amplitudes
of gluons. We observe that the class of cuts for which the method works
involves all next-to-MHV n-gluon one-loop amplitudes of any helicity
configurations. As an application of our systematic procedure, we obtain the
complete seven-gluon one-loop leading-color amplitude
A_{7;1}(1-,2-,3-,4+,5+,6+,7+).
