  We improve the linear tetrahedron method to overcome systematic errors due to
overestimations (underestimations) in integrals for convex (concave) functions,
respectively. Our method is applicable to various types of calculations such as
the total energy, the harge (spin) density, response functions, and the phonon
frequency, in contrast with the Bl\"ochl correction, which is applicable to
only the first two. We demonstrate the ability of our method by calculating
phonons in MgB$_2$ and fcc lithium.
