  Let $(G,G^\Gamma)$ be a Klein four symmetric pair. The author wants to
classify all the Klein four symmetric pairs $(G,G^\Gamma)$ such that there
exists at least one nontrivial unitarizable simple $(\mathfrak{g},K)$-module
$\pi_K$ that is discretely decomposable as a
$(\mathfrak{g}^\Gamma,K^\Gamma)$-module. In this article, three assumptions
will be made. Firstly, $G$ is an exceptional Lie group of Hermitian type, i.e.,
$G=\mathrm{E}_{6(-14)}$ or $\mathrm{E}_{7(-25)}$. Secondly, $G^\Gamma$ is
noncompact. Thirdly, there exists an element $\sigma\in\Gamma$ corresponding to
a symmetric pair of anti-holomorphic type such that $\pi_K$ is discretely
decomposable as a $(\mathfrak{g}^\sigma,K^\sigma)$-module.
