  In this paper we present the first analytic computation of the six-point
two-loop amplitude of ABJM theory. We show that the two-loop amplitude consist
of corrections proportional to two distinct local Yangian invariants which can
be identified as the tree- and the one-loop amplitude respectively. The
two-loop correction proportional to the tree-amplitude is identical to the
one-loop BDS result of N=4 SYM plus an additional remainder function, while the
correction proportional to the one-loop amplitude is finite. Both the remainder
and the finite correction are dual conformal invariant, which implies that the
two-loop dual conformal anomaly equation for ABJM is again identical to that of
one-loop N=4 SYM, as was first observed at four-point. We discuss the theory on
the Higgs branch, showing that its amplitudes are infrared finite, but equal,
in the small mass limit, to those obtained in dimensional regularization.
