Cohesive subgraph mining in hypergraphs has recently attracted increasing research attention due to its broad applicability in domains such as social networks, co-authorship networks, and recommendation systems. An important model, the hyper k-truss, is defined as a maximal cohesive subgraph in which each hyperedge is contained in at least (k-2) hyper-triangles (i.e., structures formed by three pairwise connected hyperedges). In this paper, we study the problem of hyper-truss decomposition, which aims to identify all hyper k-trusses for k ≥ 0. Due to the complex structure of hyper-triangles, the existing hyperedge-aware framework for hyper-truss decomposition incurs extra computational cost by traversing open hyper-triangles (i.e., hyper-triangles in which two hyperedges are not connected). Moreover, existing strategies enumerate all supporting hyper-triangles for each peeled hyperedge, which substantially limits overall efficiency. To address these issues, we propose a vertex-aware framework that leverages vertex-level connectivity among hyperedges. Under this framework, we design a vertex-oriented counting strategy to completely eliminate the traversal of open hyper-triangles during the counting phase and a vertex-based state propagation method to minimize the number of hyper-triangles enumerated in the peeling phase. Extensive experiments on eleven real-world datasets demonstrate the effectiveness and efficiency of our approach.