Abstract Two topologies on a set $X$ are called POequivalent if their families of preopen sets concide.
Let $P({\cal T})$ stand for the class of all topologies on X which are POequivalent to ${\cal T}$ and denote by
${\cal T}_M$ the topology on $X$ having for a base ${\cal T}_{\alpha}\cup \{\{x\}\mid \{x\}$ is closedandopen in
${\cal T}_{\gamma}\}$. It was proved in [Andrijević, M. Ganster, \emph{On $PO$equivalent topologies},
Suppl. Rend. Circ. Mat. Palermo, {\bf 24} (1990), 251256] that the class $P({\cal T})$ does not have the largest member in general.
Precisely, if $P({\cal T})$ has the largest member, say ${\cal U}$, then ${\cal U}={\cal T}_M$.
On the other hand, it was shown that ${\cal T}_M$ does not necessarily belong to $P({\cal T})$.
In this paper we are going to show that the topology ${\cal T}_M$ is actually the least upper bound of the class~$P({\cal T})$.
