The n-dimensional star graph S_n belongs to a class of bipartite graphs, and it is recognized as an attractive alternative to the hypercube. Since S₁,S₂, and S₃ have trivial structures, we focus our attention on S_n with n4 in this paper. Let F(S_n) be the set of vertex faults. Previously, it was shown that when F(S_n)n-5, S_n with n6 can embed a longest fault-free path of length at least n!-2F(S_n)-1 (respectively, n!-2F(S_n)-2) between two arbitrary vertices in different partite sets (respectively, the same partite set) [Longest fault-free paths in star graphs with vertex faults, Theoretical Computer Science 262 (2001) 215–227]. In this paper, we improve the above result by tolerating more faults (F(S_n)n-3) to embed a longest fault-free path between two arbitrary vertices in S_n, n4.