  Let $L_f$ be a link of an isolated hypersurface singularity defined by a
weighted homogenous polynomial $f.$ In this article, we give ten examples of
$2$-connected seven dimensional Sasaki-Einstein manifolds $L_f$ for which
$H_{3}(L_f, \mathbb{Z})$ is completely determined. Using the Boyer-Galicki
construction of links $L_f$ over particular K\"ahler-Einstein orbifolds, we
apply a valid case of Orlik's conjecture to the links $L_f $ so that one is
able to explicitly determine $H_{3}(L_f,\mathbb{Z}).$ We give ten such new
examples, all of which have the third Betti number satisfy $10\leq
b_{3}(L_{f})\leq 20$.
