The global consensus problem for first-order continuous-time multi-agent systems with input saturation is considered. In order to reduce the overall need of communication and system updates, we propose an event-triggered consensus protocol and a triggering law, which do not require any a priori knowledge of global network parameters. It is shown that Zeno behavior is excluded for these systems and that the underlying directed graph having a directed spanning tree is a necessary and sufficient condition for global consensus. We use a new Lyapunov function to show the sufficient condition and it inspires the triggering law. Numerical simulations are provided to illustrate the effectiveness of the theoretical results. (C) 2018 Elsevier Ltd. All rights reserved.