In this paper we study the fault diameter of the n-dimensional hypercube (or n-cube for short), Q(n), for n >= 3. Let F be a set of hybrid node-faults and/or link-faults in Q(n) such that every node of Q(n) is still connected to at least one fault-free node by a fault-free link. Then we compute the exact diameter of Q(n) - F for vertical bar F vertical bar <= 2n - 3. As an immediate consequence, our result improves upon those presented by S. Latifi (1993), in which only node-faults were addressed.