Knowledge graphs (KGs) represent known entities and their relationships using triplets, but this method cannot represent relationships between facts, limiting their expressiveness. Recently, the Bi-level Knowledge Graph (Bi-level KG) has addressed this issue by modeling facts as nodes and establishing relationships between these facts, introducing two new tasks: triplet prediction and conditional link prediction. Existing methods enhance triplets through data augmentation method and represent facts using entity representations. However, these methods do not address the isolated nodes at the structure level, nor do they effectively capture the information of facts at the feature level. To address these two issues, we design a data augmentation method that identifies islanded node by detecting anomalous structures and features in the graph. Subsequently, we perform similar subgraph matching for each isolated node to construct potential facts. To enrich the features of facts, we design a weighted combination initialization method for facts and introduce a new relation $\widetilde {R}$ , to connect facts with related entities. This approach allows for the co-training of fact and entity representations during the training process. Extensive experiments validate the effectiveness of our data augmentation and co-training methods. Our model achieves optimal performance in triplet prediction and conditional link prediction tasks.