This paper introduces a novel approach to link prediction in social networks using hyper-motif representation on hypergraphs. The authors propose the Learning Embedding based on Hyper-Motif of the Network (LEHMN) model, which diverges from traditional "node-edge" structures by modeling the network using hyper-motifs as hyper-nodes. This approach aims to better capture nuanced structural similarities between nodes that might be missed by conventional models. The LEHMN model employs the skip-gram model to learn embedding vectors based on node sequences, which are extracted using a random walk technique. To enhance the method, the authors introduce the depth and breadth motif random walk (DBMRW) strategy, which considers both connectivity and structural similarity. Experimental results on various datasets demonstrate that the proposed model outperforms state-of-the-art baselines, highlighting its robustness and effectiveness in link prediction within complex networks. The main contributions of this paper include the use of hyper-motifs for hypergraph representation, hypergraph embedding using hyper-motifs, and the application of the skip-gram model for learning embedding vectors.This paper introduces a novel approach to link prediction in social networks using hyper-motif representation on hypergraphs. The authors propose the Learning Embedding based on Hyper-Motif of the Network (LEHMN) model, which diverges from traditional "node-edge" structures by modeling the network using hyper-motifs as hyper-nodes. This approach aims to better capture nuanced structural similarities between nodes that might be missed by conventional models. The LEHMN model employs the skip-gram model to learn embedding vectors based on node sequences, which are extracted using a random walk technique. To enhance the method, the authors introduce the depth and breadth motif random walk (DBMRW) strategy, which considers both connectivity and structural similarity. Experimental results on various datasets demonstrate that the proposed model outperforms state-of-the-art baselines, highlighting its robustness and effectiveness in link prediction within complex networks. The main contributions of this paper include the use of hyper-motifs for hypergraph representation, hypergraph embedding using hyper-motifs, and the application of the skip-gram model for learning embedding vectors.