In this paper, we propose a new pattern matching algorithm based on the Franek-Jennings-Smyth (FJS) algorithm. The FJS algorithm is a hybrid of the Knuth- Morris-Pratt (KMP) and the Sunday algorithms. The worst case time complexity of the KMP algorithm is linear time and the Sunday algorithm is quadratic time. However, the Sunday algorithm is faster than the KMP algorithm in practice. Inheriting the virtues of those algorithms, the FJS algorithm runs in linear time in the worst case and fast in practice. We improve the FJS algorithm by further taking an idea inspired by the Quite-Naive algorithm by Cantone and Faro. The experimental results show that our algorithm is faster than the FJS algorithm in general except when a pattern is extremely short.