  This paper considers the problem of many-to-many disjoint paths in the
hypercube $Q_n$ with $f$ faulty vertices and obtains the following result. For
any integer $k$ with $1\leq k\leq n-2$, any two sets $S$ and $T$ of $k$
fault-free vertices in different parts of $Q_n\ (n\geq 3)$, if $f\leq 2n-2k-3$
and each fault-free vertex has at least two fault-free neighbors, then there
exist $k$ fully disjoint fault-free paths linking $S$ and $T$ which contain at
least $2^n-2f$ vertices. This result improves some known results in a sense.
