  We give a subfactor construction for a $II_{1}$ factor M which is not
anti-isomorphic to itself. The $II_{1}$ factor we consider is essentially the
same as the example previously given by Connes. However, our construction uses
the recently developed theory of free group factors. We show that there exists
an inclusion of $II_{1}$ factors $A\subset B$ which by iteration of the Jones
basic construction produces $M$ as the enveloping algebra. Here A is a free
group factor and B is isomorphic to the crossed product of A by an action of a
finite group. By using a Connes' argument involving the invariant $\chi (M)$,
we verify that $M$ is not anti--isomorphic to itself.
  Publication of this manuscript is funded in part by the National Science
Foundation. This material is based upon work supported by the National Science
Foundation under Grant No. DMS--9810361.
