Processor fault diagnosis plays an important role in multiprocessor systems for reliable computing, and the diagnosability of many well-known networks has been explored. Lai et al. proposed a novel measure of diagnosability, called conditional diagnosability, by adding an additional condition that any faulty set cannot contain all the neighbors of any vertex in a system. We make a contribution to the evaluation of diagnosability for hypercube networks under the comparison model and prove that the conditional diagnosability of n-dimensional Hypercube Q(n) is 3(n - 2) + 1 for n >= 5. The conditional diagnosability of Q. is about three times larger than the classical diagnosability of Q(n). (C) 2008 Elsevier B.V. All rights reserved.