Hypergraphs naturally capture the higher-order interactions in real-world systems. Existing edge-dependent node classification methods assign labels independently to each node-hyperedge pair, leading to potentially inconsistent label sets within the same hyperedge. To address this key issue, we formalise a more stringent task, Hyperedge-Consistent Node Classification (HC-NC), which imposes an “all-or-nothing” correctness criterion at the hyperedge level. However, solving HC-NC presents two intertwined challenges: ensuring cross-node prediction consistency and overcoming the representation dilemma in hypergraph message passing (i.e., information loss vs. connection explosion). To tackle these challenges, we propose RAHC-HPP, a framework comprising a Relation-Augmented Hypergraph Convolution network and a Hyperedge Post-Processing module. The RAHC network resolves the message-passing dilemma by enhancing star-expansion to preserve crucial information without explosive growth. Subsequently, a post-processing module, HPP, enforces internal constraints to guarantee prediction consistency. Experiments on five real-world hypergraph datasets demonstrate RAHC-HPP’s effectiveness. Our method consistently outperforms eight baseline models across datasets from different domains, achieving performance improvements of 2.6% to 45.4% over the current state-of-the-art model.