Let (A,m) be a commutative quasi-local ring with non-zero identity and let M be an Artinian co-Cohen-Macaulay R-module with Ndim M = d. Let I ⊆ m be an ideal of R with `(0 :M I) < ∞. In this paper, for 0 ≤ i ≤ d, we study the dual of Hilbert coefficients éi(I,M) of I relative to M. Also, we prove the dual of Huckaba-Marley’s inequality. Moreover, we obtain some consequences of this result,