  We derive and investigate the S-matrix for the su(2|3) dynamic spin chain and
for planar N=4 super Yang-Mills. Due to the large amount of residual symmetry
in the excitation picture, the S-matrix turns out to be fully constrained up to
an overall phase. We carry on by diagonalising it and obtain Bethe equations
for periodic states. This proves an earlier proposal for the asymptotic Bethe
equations for the su(2|3) dynamic spin chain and for N=4 SYM.
