The electronic band structure of cubic ${\mathrm{NaWO}}_{3}$ has been calculated self-consistently with the semirelativistic linear muffin-tin orbital method. The inclusion of the relativistic band shifts and the self-consistent charge transfer substantially modifies the position and width of the valence bands, bringing them into much better agreement with photoemission experiments than earlier calculations. Despite the fact that the Na 3s band lies above the Fermi level, there is a net transfer of charge of about one electron per atom to the Na sites from the W and O atoms.