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The joint entity and relation extraction task aims to extract all relational triples from a sentence. In essence, the relational triples contained in a sentence are unordered. However, previous seq2seq based models require to convert the set of triples into a sequence in the training phase. To break this bottleneck, we treat joint entity and relation extraction as a direct set prediction problem, so that the extraction model can get rid of the burden of predicting the order of multiple triples. To solve this set prediction problem, we propose networks featured by transformers with non-autoregressive parallel decoding. Unlike autoregressive approaches that generate triples one by one in a certain order, the proposed networks directly output the final set of triples in one shot. Furthermore, we also design a set-based loss that forces unique predictions via bipartite matching. Compared with cross-entropy loss that highly penalizes small shifts in triple order, the proposed bipartite matching loss is invariant to any permutation of predictions; thus, it can provide the proposed networks with a more accurate training signal by ignoring triple order and focusing on relation types and entities. Experiments on two benchmark datasets show that our proposed model significantly outperforms current state-of-the-art methods. Training code and trained models will be available at http://github.com/DianboWork/SPN4RE.