Let A be a Banach algebra with the multiplier algebra M(A). It is known that, for a closed submodule Z of A*, the quotient space A **/Z ^⊥ with the product induced by the first Arens product is a dual Banach algebra if and only if Z ⊆ WAP(A*). When M(A) is a dual Banach algebra, under some conditioins, we show that amenability of A is equivalent to Connes-amenability of A**/Z^⊥, where Z is isometrically isomorphic to some predual of M(A).
