It is shown that if two meromorphic functions \(f\) and \(g\) satisfying \[ \delta(\infty, f)= \delta(\infty, g)= 1,\quad \sum_{a\in C} \delta(a, f)+ \sum_{b\in C} \delta(b, q)> 1, \] and for some \(n\geq 1\), \(f^{(n)}\) and \(g^{(n)}\) share ICM, then either \(f^{(n)} g^{(n)}\equiv 1\) or \(f- g\equiv k\), where \(k\) is a suitable constant. This also generalizes several known results including the one obtained by the reviewer [Acta Math. Sin. 34, No. 5, 675-680 (1991; Zbl 0736.30021)].