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The authors investigate the stability for continuous-time systems with interval time-varying delay. To deal with the non-linear time-varying coefficients derived from Jensen's integral inequality, a well-known feature of the sum of these coefficients is utilised. Combining with a delay partition method, the upper bound of the derivative of the Lyapunov functional can be estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. New less conservative stability criteria are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed results.