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Computing one-loop amplitudes from the holomorphic anomaly of unitarity cuts

We propose a systematic way to carry out the method introduced in F. Cachazo, 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{sub 7;1}(1{sup -},2{sup -},3{sup -},4{sup +},5{sup +},6{sup +},7{sup +})