This paper is focused on the problem of stability for linear systems with a time-varying delay. A novel Lyapunov–Krasovskii functional that decomposed the delay in all integral terms is proposed. As a result, some less conservative stability criteria are derived by considering the relationship between time-varying delay and its intervals, which have wider application than the existing ones because independent upper bounds of the delay derivative in the various delay intervals are taken into account. Some numerical examples are finally given to show the effectiveness and the benefits of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.