The theoretical (quantum) description of large amplitude vibrations of systems containing four or more atoms using orthogonal internal coordinates requires three or more angular coordinates. The basis commonly used to represent these coordinates is the coupled angular momentum basis. We show that a direct product angular discrete variable representation (DVR) can be used advantageously, particularly for systems with high permutation-inversion symmetry and nonlinear equilibrium geometry. The DVR permits full symmetry projection and solution by the sequential diagonalization and truncation method. Application to the dimer of rigid CO2 demonstrates the accuracy and efficiency of the approach. (C) 2003 American Institute of Physics.