Let k and n(≥k+3) be two positive integers,and F be a family of meromorphic functions in unit disk Δ.If for each function f∈F,all zeros of f have multiplicity k at least,and there exist nonzero finite complex numbers b_f,c_f depending on f satisfying:b_f/c_f is a constant;min{σ(0,b_f),σ(0,c_f),σ(b_f,c_f)}≥ m,for some f^(k)－1/b_f^n-1fⁿ=c_f⇔g^(k)－1/b_g^(n-1)gⁿ=c_g,for each f,g∈F.Then F is normal in Δ.