We present a new full-potential method to solve the one-body problem, for example, in the local density approximation. The method uses the augmented plane waves (APWs) and the generalized muffin-tin orbitals (MTOs) together as basis sets to represent the eigenfunctions. Since the MTOs can efficiently describe localized orbitals, e.g, transition metal 3$d$ orbitals, the total energy convergence with basis size is drastically improved in comparison with the linearized APW method. Required parameters to specify MTOs are given by atomic calculations in advance. Thus the robustness, reliability, easy-of-use, and efficiency at this method can be superior to the linearized APW and MTO methods. We show how it works in typical examples, Cu, Fe, Li, SrTiO$_3$, and GaAs.
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