  We consider a modified version of the coproduct for $\U(\su_q(2))$ and show
that in the limit when $q \rightarrow 1$, there exists an essentially
non-cocommutative coproduct. We study the implications of this
non-cocommutativity for a system of two spin-$1/2$ particles. Here it is shown
that, unlike the usual case, this non-trivial coproduct allows for symmetric
and anti-symmetric states to be present in the multiplet. We surmise that our
analysis could be related to the ferromagnetic and antiferromagnetic cases of
the Heisenberg magnets.
