Let and be two positive integers such that . Let and be real such that and . In this note, we are mainly concerned with non-negative and classical solutions of the high-order harmonic inequality on the punctured ball . Using the method of test functions, the Hölder's inequality, and integral estimates, we will prove that this inequality has no positive solution satisfying some sufficient conditions. It should be mentioned that our result, see Theorem 1.1 in the next section, in the high-order setting is analogous to that of Laptev for the case .