  A classification is given of the exceptional $\mathbb{Z}_2 \times
\mathbb{Z}_2$-symmetric spaces $G/K$ by A.Kollross, where $G$ is an exceptional
compact Lie group or $S\!pin(8)$, and moreover the structure of $K$ is
determined as Lie algebra. In the present article, we give a pair of commuting
involutive automorphisms (involutions) $\tilde{\sigma}, \tilde{\tau}$ of $G$
concretely and determine the structure of group $G^{\sigma} \cap G^{\tau}$
corresponding to Lie algebra $\mathfrak{g}^\sigma \cap \mathfrak{g}^\tau$,
where $G$ is an exceptional compact Lie group. Thereby, we realize exceptional
$\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric spaces, globally.
