Temporal information extraction plays a critical role in natural language understanding. Previous systems have incorporated advanced neural language models and have successfully enhanced the accuracy of temporal information extraction tasks. However, these systems have two major shortcomings. First, they fail to make use of the two-sided nature of temporal relations in prediction. Second, they involve non-parallelizable pipelines in inference process that bring little performance gain. To this end, we propose a novel temporal information extraction model based on deep biaffine attention to extract temporal relationships between events in unstructured text efficiently and accurately. Our model is performant because we perform relation extraction tasks directly instead of considering event annotation as a prerequisite of relation extraction. Moreover, our architecture uses Multilayer Perceptrons (MLP) with biaffine attention to predict arcs and relation labels separately, improving relation detecting accuracy by exploiting the two-sided nature of temporal relationships. We experimentally demonstrate that our model achieves state-of-the-art performance in temporal relation extraction.