Normal family and the sequence of omitted functions

Let {f (n) } be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {h (n) } be a sequence of meromorphic functions on D, whose poles are multiple, such that {h (n) } converges locally uniformly in the spherical metric to a function h which is meromorphic and zero-free on D. If f' (n) not equal h (n) , then {f (n) } is normal on D.