  The following sharpening of Tur\'an's theorem is proved. Let $T_{n,p}$ denote
the complete $p$--partite graph of order $n$ having the maximum number of
edges. If $G$ is an $n$-vertex $K_{p+1}$-free graph with $e(T_{n,p})-t$ edges
then there exists an (at most) $p$-chromatic subgraph $H_0$ such that
$e(H_0)\geq e(G)-t$.
  Using this result we present a concise, contemporary proof (i.e., one
applying Szemer\'edi's regularity lemma) for the classical stability result of
Simonovits.
