We present a new model for the rotation-vibration motion of pyramidal XY3 molecules, based on the Hougen-Bunker-Johns approach. Inversion is treated as a large-amplitude motion, while the small-amplitude vibrations are described by linearized stretching and bending coordinates. The rotation-vibration Schrödinger equation is solved variationally. We report three applications of the model to 14NH3 using an analytic potential function derived from high-level ab initio calculations. These applications address the J = 0 vibrational energies up to 6100cm, the J ≤ 2 energies for the vibrational ground state and the ν2, vν4, and 2ν2 excited vibrational states, and the J ≤ 7 energies for the 4ν2+ vibrational state. We demonstrate that also for four-atomic molecules, theoretical calculations of rotation-vibration energies can be helpful in the interpretation and assignment of experimental, high-resolution rotation-vibration spectra. Our approach incorporates an optimum inherent separation of different types of nuclear motion and thus remains applicable for rotation-vibration states with higher J values where alternative variational treatments are no longer feasible.