  Let $D(H)$ be the quantum double associated to a finite dimensional
quasi-Hopf algebra $H$. In this note, we first generalize a result of Majid,
stating that a finite dimensional Hopf algebra $H$ is quasitriangular if and
only if there is a projection of the quantum double $D(H)$ onto $H$ covering
the natural inclusion.We then prove that the quantum double of a finite
dimensional quasitriangular quasi-Hopf algebra is a biproduct.
