In this brief, the output regulation problem of fully distributed linear heterogeneous multi-agent systems via event-triggered communication is investigated. A novel information acquisition scheme is proposed, which can effectively save the computing resources of the controller. The time-invariant matrix $S$ is obtained directly through completely distributed communication. Therefore, the computational burden caused by the introduction of matrix observer is reduced. At the same time, to save communication resources, this brief adopts a communication scheme and designs a Zeno-free event-triggered mechanism for each agent. The trigger mechanism in this brief can avoid the continuous monitoring of the system state, and does not need to supplement the self-triggering algorithm. In addition, the control strategy designed in this brief is fully distributed with fixed parameters, and the use of global information can be avoided without using dynamic parameters in the controller. Finally, a numerical example is given to verify the effectiveness of the proposed method.