  We show how the holomorphic anomaly found in hep-th/0409245 can be used to
efficiently compute certain classes of unitarity cuts of one-loop N=4
amplitudes of gluons. These classes include all cuts of n-gluon one-loop MHV
amplitudes and of n-gluon next-to-MHV amplitudes with helicities
(1+,2+,3+,4-,..., n-). As an application of this method, we present the
explicit computation of the (1,2,3)-cut of the n-gluon one-loop N=4
leading-color amplitude A_{n;1}(1+,2+,3+,4-,..., n-). The answer is given in
terms of scalar box functions and provides information about the corresponding
amplitudes. A possible way to generalize this method to all kinds of unitarity
cuts is also discussed.
