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 <= k= 2), if f <= 2n - 2k - 2 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. A linear algorithm for finding such disjoint paths is also given. This result improves some known results in a sense. (C) 2016 Elsevier B.V. All rights reserved.