A growing interest emerges in event extraction which aims to extract multiple events with triggers and arguments. Previous methods mitigate the problem of multiple events extraction by predicting the arguments conditioned on the event trigger and event type, assuming that these arguments belong to a single event. However, the assumption is invalid in general as there may be multiple events. Therefore, we present a unified framework called MatEE for trigger-sharing events extraction. It resolves the kernel bottleneck by effectively modeling the relations between arguments by an event matrix, where trigger-sharing events are represented by multiple cliques. We verify the proposed method on 3 widely-used benchmark datasets of event extraction. The experimental results show that it beats all the advanced competitors, significantly improving the state-of-the-art performances in event extraction.