This paper focuses on how to extract multiple relational facts from unstructured text. Neural encoder-decoder models have provided a viable new approach for jointly extracting relations and entity pairs. However, these models either fail to deal with entity overlapping among relational facts, or neglect to produce the whole entity pairs. In this work, we propose a novel architecture that augments the encoder and decoder in two elegant ways. First, we apply a binary CNN classifier for each relation, which identifies all possible relations maintained in the text, while retaining the target relation representation to aid entity pair recognition. Second, we perform a multi-head attention over the text and a triplet attention with the target relation interacting with every token of the text to precisely produce all possible entity pairs in a sequential manner. Experiments on three benchmark datasets show that our proposed method successfully addresses the multiple relations and multiple entity pairs even with complex overlapping and significantly outperforms the state-of-the-art methods.