  Let $(R,\mathfrak{m})$ be a regular local ring containing a field $K$. Let
$I$ be a Cohen-Macaulay ideal of height $g$. If $\text{char } K = p > 0$ then
by a result of Peskine and Szpiro the local cohomology modules $H^i_I(R)$
vanish for $i > g$. This result is not true if $\text{char } K = 0$. However we
prove that the Bass numbers of the local cohomology module $H^g_I(R)$
completely determine whether $H^i_I(R)$ vanish for $i > g$.
