  After reduction techniques, two-loop amplitudes in N=4 super Yang-Mills
theory can be written in a basis of integrals containing scalar double-box
integrals with rational coefficients, though the complete basis is unknown.
Generically, at two loops, the leading singular behavior of a scalar double box
integral with seven propagators is captured by a hepta-cut. However, it turns
out that a certain class of such integrals has an additional propagator-like
singularity. One can then formally cut the new propagator to obtain an octa-cut
which localizes the cut integral just as a quadruple cut does at one-loop. This
immediately gives the coefficient of the scalar double box integral as a
product of six tree-level amplitudes. We compute, as examples, several
coefficients of the five- and six-gluon non-MHV two-loop amplitudes. We also
discuss possible generalizations to higher loops.
