Let F be a family of meromorphic functions in a domain D,let k≥2,m be two positive in tegers.Let a ≠0,b be two finite complex numbers;and let c(z) be a function holomorphic in D such that c(z) ≠0 for z∈D.If,for every f∈F,all zeros of f(z) have multiplicity ≥m,the number of all poles of f′(z) in D is at most m and f(z)=af(z)=b,f(z)=0f′(z)=c(z),f′(z)=c(z)|f~((k))(z)|≤h,then F is normal in D.