  In this article, we focus on $L^{2}(\mathbb{R}^d)\times\cdots\times
L^{2}(\mathbb{R}^d)\rightarrow L^{2/m}(\mathbb{R}^d)$ estimates for multilinear
maximal averages over non-degenerate hypersurfaces. Our findings is new for
$m$-linear averages with $m\geq3$, and represent a reproof of the recent result
of T. Borges, B. Foster, and Y. Ou on the curvature conditions of the
hypersurfaces required in establishing $L^{2}(\mathbb{R}^d)\times
L^{2}(\mathbb{R}^d)\rightarrow L^{1}(\mathbb{R}^d)$ estimates of bilinear
maximal functions.
