  We construct the Drinfeld twists (factorizing $F$-matrices) of the
$gl(m|n)$-invariant fermion model. Completely symmetric representation of the
pseudo-particle creation operators of the model are obtained in the basis
provided by the $F$-matrix (the $F$-basis). We resolve the hierarchy of the
nested Bethe vectors in the $F$-basis for the $gl(m|n)$ supersymmetric model.
