  In \cite{Lusztig}, Lusztig gives an explicit formula for the bijection
between the set of bipartitions and the set $\mathcal{N}$ of unipotent classes
in a spin group which carry irreducible local systems equivariant for the spin
group but not equivariant for the special orthogonal group. The set
$\mathcal{N}$ has a natural partial order and therefore induces a partial order
on bipartitions. We use the explicit formula given in \cite{Lusztig} to prove
that this partial order on bipartitions is the same as the dominance order
appeared in Dipper-James-Murphy's work.
