  Given a finite dimensional algebra $C$ (over an algebraically closed field)
of global dimension at most two, we define its relation-extension algebra to be
the trivial extension $C\ltimes \Ext_C^2(DC,C)$ of $C$ by the $C$-$C$-bimodule
$\Ext_C^2(DC,C)$. We give a construction for the quiver of the
relation-extension algebra in case the quiver of $C$ has no oriented cycles.
Our main result says that an algebra $\tilde C$ is cluster-tilted if and only
if there exists a tilted algebra $C$ such that $\tilde C$ is isomorphic to the
relation-extension of $C$.
