Plane waves and Confined Localized Orbitals have been used to construct a new mixed basis for electronic structure calculations. Confinement is a mathematical transformation which smoothly suppresses the tails of the atomic orbitals. This eliminates multicentre integrals in the expressions for the matrix elements. Using self-consistent potentials supplied by the linear muffin tin orbital method (LMTO) we have calculated the bulk band structures of Al, Si, Cu, and LiH to a degree of accuracy comparable with the results given by the LMTO calculations. The basis functions are energy independent so the full solution is obtained without invoking any kind of linearization scheme.