An improved ‘‘tight‐binding’’ Hamiltonian matrix which accounts for the effects of a space‐dependent effective‐mass is formulated. The matrix elements are derived for a single‐particle effective‐mass Hamiltonian in the nearest‐neighbor approximation. In contrast to previous work, the derivation given here strictly preserves the Hermicity of the original continuous‐space Hamiltonian from which the tight‐binding Hamiltonian is derived.