A new basis-set representation of the vibration/rotation eigenfunctions of triatomic molecules in mass-scaled Jacobi coordinates is presented. The basis is a nondirect product, consisting of radial basis functions in which the centers and ``shapes'' are functions of the angular variable. The functional dependence of these parameters is arbitrary, thus giving the method the ability to move the radial basis anywhere in the angular space. This results in a basis with the potential to describe considerable coordinate-coordinate correlation. The advantage of this is noted in the context of a new formulation of self-consistent field theory, in which a single product function of the above type is variationally optimized. A simple version of the theory, in which only one basis is movable, is applied to two model potentials representing isomerization. The convergence properties are shown to be dramatically better than those using a conventional direct-product basis, especially for delocalized states, and for the model potential with large curvature.