  We reformulate the nested coordinate Bethe ansatz in terms of coproducts of
Yangian symmetry generators. This allows us to derive the nested Bethe
equations for the bound state string S-matrices. We find that they coincide
with the Bethe equations obtained from a fusion procedure. The bound state
number dependence in the Bethe equations appears through the parameters x^{\pm}
and the dressing phase only.
