  The balanced hypercube $BH_n$, a variant of the hypercube, was proposed as a
desired interconnection network topology. It is known that $BH_n$ is bipartite.
Assume that $S=\{s_1,s_2,\cdots,s_{2n-2}\}$ and $T=\{t_1,t_2,\cdots,t_{2n-2}\}$
are any two sets of vertices in different partite sets of $BH_n$ ($n\geq2$). It
has been proved that there exists paired 2-disjoint path cover of $BH_n$. In
this paper, we prove that there exists unpaired $(2n-2)$-disjoint path cover of
$BH_n$ ($n\geq2$) from $S$ to $T$, which improved some known results. The upper
bound $2n-2$ of the number of disjoint paths in unpaired $(2n-2)$-disjoint path
cover is best possible.
