The augmented-plane-wave method for energy-band calculations is presented in a form which handles a general one-electron crystalline potential, rather than the restricted "muffin-tin" potential which has traditionally been used. From the wave functions resulting from the band calculation, the total crystalline charge density is found, and from this, a new potential is found, making an iterative self-consistent calculation possible. As an example, the method has been applied to body-centered cubic (bcc) lithium. The results of two energy-band calculations are reported. One used the average free-electron-exchange approximation suggested by Slater. The second used two-thirds of this exchange. © 1969 The American Physical Society.