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In this paper, the problem of stability analysis for linear continuous-time systems with constant discrete and distributed delays is investigated. First, an improved reciprocally convex lemma is presented, which is a generalization of the existing reciprocally convex inequalities and can be directly applied in the case that of the delay interval is divided into <inline-formula> <tex-math notation="LaTeX">$N\geq 2$ </tex-math></inline-formula> subintervals. Second, combining this with the auxiliary functions-based integral inequalities and the delay partition approach, a novel stability criterion of delay systems is given in terms of linear matrix inequalities. Finally, three numerical examples are given and their results are compared with the existing results. The comparison shows that the stability criterion proposed in this paper can provide larger upper bounds of delay than the other ones.