High Average Utility Itemset (HAUI) mining (HAUIM) is an important task in data mining, as it has practical applications in diverse domains. To design efficient algorithms for HAUIM, researchers need to utilize upper bounds (UB) and weak upper bounds (WUB), along with corresponding pruning strategies, to early eliminate low average utility itemsets (LAUIs). This is necessary due to the fact that the average utility function fails to satisfy the anti-monotonic property. While many UBs and WUBs have been proposed so far, their values remain rather loose when compared to the average utility, leading to the limited efficiency of corresponding algorithms. To address this issue, this paper proposes a novel algorithm called MHAUI- TWUB, which efficiently discovers all HAUIs. The proposed algorithm introduces a novel vertical WUB named tvwaub, and employs an efficient pruning strategy to swiftly eliminate a significant number of LAUIs in the early stages of the mining process. Experimental evaluations demonstrate that the proposed algorithm outperforms state-of-the-art algorithms in terms of runtime, memory usage, and the number of join operations.