The algorithm for L-2-optimal model reduction described in Krajewski et al. (1995), though computationally efficient, may sometimes fail to converge. In this note, it is shown that, by exploiting the bounds on the eigenvalues of the Jacobian of the associated transition function, a variant can be developed whose convergence to the minima of the considered index is guaranteed. The resulting algorithm requires a small additional amount of computation with respect to the original procedure.