Joint entity and relation extraction aims to extract relation triplets from plain text directly. Prior work leverages Sequence-to-Sequence (Seq2Seq) models for triplet sequence generation. However, Seq2Seq enforces an unnecessary order on the unordered triplets and involves a large decoding length associated with error accumulation. These methods introduce exposure bias, which may cause the models overfit to the frequent label combination, thus limiting the generalization ability. We propose a novel Sequence-to-UnorderedMulti-Tree (Seq2UMTree) model to minimize the effects of exposure bias by limiting the decoding length to three within a triplet and removing the order among triplets. We evaluate our model on two datasets, DuIE and NYT, and systematically study how exposure bias alters the performance of Seq2Seq models. Experiments show that the state-of-the-art Seq2Seq model overfits to both datasets while Seq2UMTree shows significantly better generalization. Our code is available at https://github.com/WindChimeRan/OpenJERE.