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This paper is devoted to the study of delay-dependent stability of time-varying delay systems. A delay-derivative-partitioning approach is proposed. By constructing an augmented Lyapunov functional that contains two delay-product-dependent terms and using the delay-derivative-partitioning approach, an improved stability condition is established. The derived condition is described as a set of linear matrix inequalities, which can be readily implemented. Finally, four examples are carried out so as to attest the effect and merit of the presented approach.