  Let $\D$ be a $(d-1)$-dimensional pure $f$-simplicial complex over vertex set
$[n]$. In this paper, it is proved that $n=2d$ holds true if $\D$ is minimal
Cohen-Macaulay. It is also indicated that the recent work of \cite{Dao2020}
implies that shellable condition on a pure simplicial complex $\D$ is identical
with CM properties of a full series of subcomplexes of $\D$.
