Using a Green's function approach, we present an alternate derivation of the R-matrix propagation equations. We also present an extension of the method which employs a basis set expansion for both translational and target motions within each R-matrix sector. This new approach is then investigated in comparison to the original close-coupling approach, studying a model collinear vibrational excitation problem. The new approach allows much larger R-matrix boxes to be used in regions of configuration space where the potential is changing rapidly with the scattering coordinate. © 1979 American Institute of Physics.