A vibration-rotation Hamiltonian for a symmetric triatomic molecule, based upon a stretch-bender reference frame has been derived. This frame is chosen so that as the molecule bends the reference geometry follows the minimum in the potential energy surface, thus minimizing the size of the displacements required to reach the instantaneous axis geometry. This may be regarded as an extension of methods based upon the rigid-bender reference frame approach developed by Hougen, Bunker, and Johns [J. Mel. Spectrosc. 34, 136 (1970)]. This new stretch-bender Hamiltonian is combined with the Barrow, Dixon, and Duxbury [Mel. Phys. 27, 1217 (1974)] and the Jungen and Merer [Mel. Phys. 40, 25 (1980)] methods of solving the Renner-Teller coupling problem in which molecules execute large amplitude nuclear motion, producing a compact method for the variational calculation of the energies of such a system. The (a) over tilde (1)A(1) and (b) over tilde B-1(1) states of the methylene radical, CH2, are used to demonstrate the use of this method for the analysis of the behavior of strongly coupled electronic and vibrational states.