We show that the expression for the supersymmetric partition function of the chiral unitary (Laguerre) ensemble conjectured recently by Splittorff and Verbaarschot [Phys. Rev. Lett.90, 041601 (2003)] follows from the general expression derived recently by Fyodorov and Strahov [J. Phys. A: Math. Gen.36, 3203 (2003)].