Joint extraction of entity and relation represents a critical component in natural language processing, exerting a direct influence on the quality of ensuing knowledge graph construction. Although existing methodologies for the joint extraction of entities and relations have demonstrated promising results, exemplified by the parallel triplet decoding method which generates final triplets via ensemble prediction, these approaches often neglect the interactions between entities and relationships. To address this issue, we introduce a dual set prediction network, enhanced with a self-prior attention mechanism (SADSPN).In order to bolster the interactions between entities and relationships, our approach utilizes parallel decoding of triplets via dual set prediction networks, incorporating a self-prior attention mechanism within both networks to intensify the model's emphasis on pivotal information. The initial set prediction network decodes the subject-object information contained within triplets, whereas the second network models the embedded triplets, using the subject-object information to decipher the types of relationships between them. Utilizing a pretrained BERT encoder, our model attains F1 scores of 93.1% and 93.7% on the extensively employed NYT and WebNLG datasets. Additionally, the model exhibits exceptional performance in analyzing overlapping triplets.