AbstractVery high computational efficiencies have been achieved recently by introducing higher order approximations to nodal formalisms for the discrete ordinates, neutron transport equation. However, the difficulty of the nodal formalism, its final discrete variable equations, and the solution algorithms have limited the usefulness and applicability of nodal methods in spite of their extremely high accuracy.A general order, general dimensionality nodal transport method cast in a simple, compact, singleweight, weighted diamond-difference form is derived. The new form is a consistently formulated nodal method, which can be solved using either the discrete nodal-transport method or the nodal-equivalent finite difference algorithms without any approximations. The final discrete variable equations for the two-dimensional case are implemented in a computer code to solve monoenergetic, isotropic scattering, external source problems to any given order, i.e., C-C, L-L, Q-Q, etc. A simple test problem with large homogeneous regions is solved using this code, on meshes ranging from 2×2 to 128×128, and orders ranging from zero to nine. The results show that, for this problem, the CPU time and the storage size required to achieve a given accuracy decrease monotonically up to order five. Hence, very high order methods may be more computationally efficient in solving practical problems with large homogeneous regions.