The tight-binding method attempts to represent the electronic structure of condensed matter using a minimal atomic-orbital like basis set. To compute tight-binding overlap and Hamiltonian matrices directly from first-principles calculations is a subject of continuous interest. Usually, first-principles calculations are done using a large basis set or long-ranged basis set (e.g. muffin-tin orbitals (MTOs)) in order to get convergent results, while tight-binding overlap and Hamiltonian matrices are based on a short-ranged minimal basis representation. In this regard, a transformation that can carry the electronic Hamiltonian matrix from a large or long-ranged basis representation onto a short-ranged minimal basis representation is necessary to obtain an accurate tight-binding Hamiltonian from first principles. The idea of calculating tight-binding matrix elements directly from a first-principles method was proposed by Andersen and Jepsen in 1984 [1]. They developed a scheme which transforms the electronic band structures of a crystal calculated using a long-ranged