We prove that the type ${\mathrm{II}}_1$ factor $L\left(F\right)$ generated by the regular representation of $F$ is isomorphic to its tensor product with the hyperfinite type ${\mathrm{II}}_1$ factor. This implies that the unitary group of $L\left(F\right)$ is contractible with respect to the topology defined by the natural Hilbertian norm.