The authors discuss the normality concerning holomorphic functions and get the following result.Let (F) be a family of functions holomorphic on a domain D ? C,all of whose zeros have multiplicity at least k,where k ≥ 2 is an integer.Let h(z) (≠) 0 and ∞ be a meromorphic function on D.Assume that the following two conditions hold for every f ∈ F:(a) f(z) =0( →) |f(k)(z)| ＜ |h(z)|.(b) f(k)(z) ≠ h(z).Then F is normal on D.