The star graph Sn has been recognized as an attractive alternative to the hypercube. Since S1, S2, and S3 have trivial structures, we focus our attention on Sn with n ≥ 4 in this paper. Let Fv denote the set of faulty vertices in Sn. We show that when |Fv| ≤ n - 5 ,Sn with n ≥ 6 contains a fault-free path of length n! - 2|Fv| - 2 (n! - 2 |Fv| - 1) between arbitrary two vertices of even (odd) distance. Since Sn is bipartite with two partite sets of equal size, the path is longest for the worst-case scenario. The situation of n ≥ 4 and |Fv| ≥ n - 5 is also discussed.