  The unitarity condition for scattering amplitudes in a non-anticommutative
quantum field theory is investigated. The Cutkosky rules are shown to hold for
Feynman diagrams in Euclidean momentum space and unitarity of amplitudes can be
satisfied. An analytic continuation of the diagrams to physical Minkowski
spacetime can be performed without invoking unphysical singularities in
amplitudes. The high energy behavior of amplitudes is found to be regular at
infinity provided that only space-space non-anticommutativity is allowed.
