  Let $\cal A$ be a Banach algebra. We study those closed ideals $I$ of $\cal
A$ for which the first cohomology group of $\cal A$ with coefficients in $I^*$
is trivial; i.e. $H^1(\cal A,I^*)=\{0\}$. We investigate such closed ideals
when $\cal A$ is weakly amenable or biflat. Also we give some hereditary
properties of ideal amenability.
