A generalized non‐muffin‐tin band structure method is presented in the context of multiple scattering off of the Wigner–Seitz cell. This technique has the following desirable features: it is formally exact and rapidly convergent; it preserves the separation between the nondiagonal scattering matrix for the cell and the usual structure constants of KKR in the secular determinant; it produces an accurate representation of the wave function throughout the sphere bounding the Wigner–Seitz cell and hence is suitable for self‐consistent field calculations and applications that require a detailed knowledge of the unperturbed crystal potential and wave functions. Various aspects of the application of this theory to the empty lattice and sodium are presented, and its limitations discussed. Some future lines of research are briefly reviewed. Copyright © 1984 John Wiley & Sons, Inc.