Extracting event relations that deviate from known schemas has proven challenging for previous methods based on multi-class classification, MASK prediction, or prototype matching. Recent advancements in large language models have shown impressive performance through instruction tuning. Nevertheless, in the task of event relation extraction, instruction-based methods face several challenges: there are a vast number of inference samples, and the relations between events are non-sequential. To tackle these challenges, we present an improved instruction-based event relation extraction framework named MAQInstruct. Firstly, we transform the task from extracting event relations using given event-event instructions to selecting events using given event-relation instructions, which reduces the number of samples required for inference. Then, by incorporating a bipartite matching loss, we reduce the dependency of the instruction-based method on the generation sequence. Our experimental results demonstrate that MAQInstruct significantly improves the performance of event relation extraction across multiple LLMs.