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This study reconsiders the problem of reachable set bounding for a class of linear systems in the presence of both discrete and distributed delays. Some new criteria are established where the useful term is retained when we estimate the upper bound of the derivative of the Lyapunov-Krasovskii functional. The free-weighting matrix technique is utilised to realise such a purpose. Moreover, the special structure constraint on the final expression of the derivative of the Lyapunov functional in the previous result of authors is removed. Consequently, a tighter bound of the reachable set is obtained. Numerical examples are given to illustrate the merit of the proposed method comparing with the existing ones.