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This note is concerned with event-triggered H∞ controller design for networked control systems. A novel event-triggering scheme is proposed, which has some advantages over some existing schemes. A delay system model for the analysis is firstly constructed by investigating the effect of the network transmission delay. Then, based on this model, criteria for stability with an H∞ norm bound and criteria for co-designing both the feedback gain and the trigger parameters are derived. These criteria are formulated in terms of linear matrix inequalities. Simulation results have shown that the proposed event-triggering scheme is superior to some existing event-triggering schemes in the literature.