  We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF)
model by calculating the three-particle scattering amplitude at the first
non-trivial order and showing that the S-matrix is factorizable at this order.
We consider a more general fermionic model and find a necessary constraint to
ensure its integrability at quantum level. We then show that the quantum
integrability of the AAF model follows from this constraint. In the process, we
also correct some missed points in earlier works.
