  We study the conditions under which the highest nonvanishing local cohomology
module of a domain $R$ with support in an ideal $I$ is faithful over $R$, i.e.,
which guarantee that $H^c_I(R)$ is faithful, where $c$ is the cohomological
dimension of $I$. In particular, we prove that this is true for the case of
positive prime characteristic when $c$ is the number of generators of $I$.
