  We present a detailed construction of a completely symmetric representation
of the monodromy matrix by the use of Drinfel'd twists for the rational $sl(3)$
Heisenberg model without refering to the special symmetry of the model. With
the help of this representation we are able to resolve the hierarchy of the
nested Bethe wavevectors for the $sl(3)$ invariant rational Heisenberg model.
