The Hartree‐Fock band structures of krypton and xenon are calculated from first principles, using the Gaussian orthogonalized plane wave method. This method, which exploits the Gaussian representation of occupied orbitals, allows to include the exchange potential in its nonlocal from. As a side‐product, it is shown that some drawbacks, erroneously attributed to the OPW method, disappear if appropriate care is done in describing core states and the consequent orthogonalization effects.