Summary: We study the uniqueness of entire functions and prove the following result: Let \(f(z)\) and \(g(z)\) be two nonconstant entire functions, \(n\geq 7\) a positive integer, and let \(a\) be a nonzero finite complex number. If \(f^n(z)(f(z)-1)f'(z)\) and \(g^n(z)(g(z)-1)g'(z)\) share \(a\) CM, then \(f(z)\equiv g(z)\). The result improves the theorem due to \textit{M.-L. Fang} and \textit{W. Hong} [Indian J. Pure Appl. Math. 32, No. 9, 1343--1348 (2001; Zbl 1005.30023)].