This paper studies the response time bound of a DAG (directed acyclic graph) task. Recently, the idea of using multiple paths to bound the response time of a DAG task, instead of using a single longest path in previous results, was proposed and leads to the so-called multi-path bound. Multi-path bounds can greatly reduce the response time bound and significantly improve the schedulability of DAG tasks. This paper derives a new multi-path bound and proposes an optimal algorithm to compute this bound. We further present a systematic analysis on the dominance and the sustainability of three existing multi-path bounds and the proposed multi-path bound. Our bound theoretically dominates and empirically outperforms all existing multi-path bounds. What's more, the proposed bound is the only multi-path bound that is proved to be self-sustainable.