In this paper, the authors study the uniqueness of meromorphic functions sharing a nonzero finite value. The results in this paper improve some results given by Xu (Comput. Math. Appl. 59:9-17, 2010), Fang (Comput. Math. Appl. 44:823-831, 2002), Chen (Comput. Math. Appl. 56:3000-3014, 2008) and Banerjee (lnt. J. Pure Appl. Math. 48:41-56, 2008).