Large-amplitude vibrations of the symmetric triatomic molecule are considered as the coupled rotations of two diatomic fragments. This procedure does not require a molecule-fixed coordinate system to be defined. Thus Eckart conditions, Coriolis coupling, and similar concerns are avoided. An algebraic approach is used to generate a Hamiltonian which describes the stretching vibrations and a second Hamiltonian which describes the bend. A model potential is used which treats the stretches as coupled Morse oscillators and the bend as a bond-length-dependent anharmonic oscillator. This paper gives detailed results only for states of zero angular momentum. However it can be used for all rotational states.