  We call a function $f$ in $C(X)$ to be hard-bounded if $f$ is bounded on
every hard subset, a special kind of closed subset, of $X$. We call a subset
$T$ of $X$ to be $S$-embedded if every hard-bounded continuous function of $T$
can be continuously extended upto $X$. Every $S$-embedded subset is
$C^*$-embedded. In this paper we have given a characterization of the converse
part. To get the converse, we came across a type of function which are bounded
away from zero on every hard subset of a subset. We further studied few
properties of this type of functions and also of hard-bounded functions.
