  Let $R$ be a Cohen-Macaulay local ring, $I$ a strongly Cohen-Macaulay ideal
of $R$. We show that $R/{\rm Ann}_R(I)$ is a maximal Cohen-Macaulay $R$-module
by means of the delta-invariant. Also it is shown that there exists a
Cohen-Macaulay ideal $J$ of $R$ such that the $\delta_{R/J}$-invariant of all
Koszul homologies of $R$ with respect $I$ is zero.
