May happen in parallel (MHP) analysis decides whether a pair of statements in a parallel program can be executed concurrently; it plays an important part in parallel analyses. This paper proposes a novel may-happen-in-parallel analysis algorithm for Java programs. Compared with the existing MHP algorithm, the new alogrithm discards the unnecessary assumption that a child thread can only be join-synchronized by its parent thread, and processes start-synchronization and join-synchronization independently in a decoupled way. This makes the processing logic of the algorithm more concise and more complete than that of the existing algorithm. When computing dominator information, the new algorithm has better scalability for it does not need to construct the global flow graph for the program by inlining, which is needed by the existing algorithms. The new MHP analysis algorithm is used to sift false warnings reported by a static data race detection tool. The experimental results on 14 Java programs show that the time of computing dominator information of the new MHP analysis is much shorter than that of the existing algorithm.