Extracting relational triples from a piece of text is an essential task in knowledge graph construction. However, most existing methods either identify entities before predicting their relations, or detect relations before recognizing associated entities. This order may lead to error accumulation because once there is an error in the initial step, it will accumulate to subsequent steps. To solve this problem, we propose a parallel model for jointly extracting entities and relations, called PRE-Span, which consists of two mutually independent submodules. Specifically, candidate entities and relations are first generated by enumerating token sequences in sentences. Then, two independent submodules (Entity Extraction Module and Relation Detection Module) are designed to predict entities and relations. Finally, the predicted results of the two submodules are analyzed to select entities and relations, which are jointly decoded to obtain relational triples. The advantage of this method is that all triples can be extracted in just one step. Extensive experiments on the WebNLG*, NYT*, NYT and WebNLG datasets show that our model outperforms other baselines at 94.4%, 88.3%, 86.5% and 83.0%, respectively.