Hyperedge prediction plays a critical role in high-order relational modeling with hypergraphs, yet most existing methods primarily focus on sampling strategies or local aggregation within candidate hyperedges. These approaches often overlook global structural dependencies that are essential for learning expressive node and hyperedge representations. In this paper, we propose HyperNoRA, a novel self-supervised hypergraph learning framework that integrates global node-level relation awareness with contrastive learning. Specifically, we construct a global node relation graph that captures both direct and indirect structural correlations, which guides a structure-aware aggregator to enhance node representations with informative global context. To prevent over-smoothing and maintain discriminability, a contrastive learning module is introduced to align representations across graph augmentations while separating semantically dissimilar nodes. Extensive experiments on several benchmark datasets demonstrate that HyperNoRA consistently outperforms state-of-the-art baselines, and ablation studies verify the effectiveness of its key components.