  Let $(R,\m)$ be an analytically unramified Cohen-Macaulay local ring of
dimension 2 with infinite residue field and $\ov{I}$ be the integral closure of
an ideal $I$ in $R$. Necessary and sufficient conditions are given for
$\ov{I^{r+1}J^{s+1}}=a\ov{I^rJ^{s+1}}+b\ov{I^{r+1}J^s}$ to hold ${for all}r
\geq r_0{and}s \geq s_0$ in terms of vanishing of
$[H^2_{(at_1,bt_2)}(\ov{\mathcal{R}^\prime}(I,J))]_{(r_0,s_0)}$, where $a \in
I,b \in J$ is a good joint reduction of the filtration $\{\ov{I^rJ^s}\}.$ This
is used to derive a theorem due to Rees on normal joint reduction number zero.
The vanishing of $\ov{e}_2(IJ)$ is shown to be equivalent to Cohen-Macaulayness
of $\ov{\mathcal{R}}(I,J)$.
