This paper deals with a coupled system of fourth-order parabolic inequalities ｜u｜t ≥ -△2^u＋｜v｜^q, ｜v｜t ≥-△2v＋｜u｜p^ in S=R^n ×R^＋ withp, q 〉 1, n ≥1. AFujita- Liouville type theorem is established that the inequality system does not admit nontrivial nonnegative global solutions on S whenever n/4≤ max（ p＋1/pq-1, q＋1/pq-1 ）. Since the general maximum-comparison principle does not hold for the fourth-order problem, the authors use the test function method to get the global non-existence of nontrivial solutions.
