By using some fundamental knowledge,research methods and research results about the theories of value distribution and normal family for meromorphic functions and based on one result of Xu Chengyu,Liu Xiaojun's theorem,and by further considering the condition that the exceptional function is a rational function,the following result was achieved:let f be a transcendental meromorphic function on C,if there exists M ≥ 0 such that for f=0⇒|z²f'|≤ M,all zeros of f are real zeros and all of whose poles have multiplicity at least 3,then f'-1/(z²) has infinite number of zeros.