  We consider weighted Bergman projection $P_{\alpha}: L^{\infty}(\Bbb B)
\rightarrow {\cal B} $ where $\alpha>-1$ and $\cal B$ is the Bloch space of the
unit ball $\Bbb B$ of the complex space $\Bbb C^n.$ We obtain the exact norm of
the operator $P_{\alpha}$ where the Bloch space is observed as a space with
norm (and semi-norm) induced from the Besov space
$B_{p},0<p<\infty,(B_{\infty}=\cal B).$ Our work contains, as a special case,
the main results from \cite{Kalaj} and \cite{Ant}.
