A new method for approximating anisotropic, multi-group scatter cross sections for use in discretized and Monte Carlo multi-group neutron transport is presented. The new method eliminates unphysical artifacts such as negative group scatter cross sections and falsely positive cross sections. Additionally, when combined with the discrete elements angular quadrature method, the new cross sections eliminate the lack of angular support in the discrete ordinates quadrature method. The new method generates piecewise-average group-to-group scatter cross sections. The accuracy and efficiency for calculating the discrete elements cross sections has improved by many orders of magnitude compared to DelGrande and Mathews (7) previous implementation. The new cross sections have extended the discrete elements method to all neutron-producing representations in the Evaluated Nuclear Data Files (13). The new cross section method has been validated and tested with the cross section generation code, NJOY (13). Results of transport calculations using discrete elements, discrete ordinates, and Monte Carlo methods for two, one-dimensional slab geometry problems are compared.