In a recent article [J. Chem. Phys. 118, 6946 (2003)], X.-G. Wang and T. Carrington, Jr. presented an efficient method for computing the vibrational bend levels of five-atom molecules. The method is particularly useful if four of the five atoms are identical, in which case G(4) symmetry may be exploited in conjunction with the iterative symmetry-adapted Lanczos method. In this paper, we demonstrate how to extend the group of exploitable symmetry operations to G(12), without compromising any of the desirable numerical features of the Wang and Carrington approach. This reduces total CPU effort by at least a factor of 3. (C) 2003 American Institute of Physics.