This paper studies the uniqueness of meromorphic functions f n ∏ k i=1 (f (i) ) ni and g n ∏ k i=1 (g (i) ) ni that share two values, where n, nk, k ∈ N, ni ∈ N ∪ {0}, i = 1, 2, . . . , k − 1. The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012).