The electronic band structure of the InAs-GaSb superlattice is studied within the localized-orbital framework by the renormalization method. The tight-binding Hamiltonian includes spin-orbit coupling and an accurate description of the composing crystals near relevant band edges. The tight-binding renormalization-group method is described in detail, and is shown to be conceptually simple and operatively efficient. The superlattice band structure is calculated for several unit-cell widths, and the semiconductor-semimetal transition is analyzed. A negative indirect band gap appears for long-period superlattices; its origin and the effects of band anisotropy and spin-orbit splitting are discussed.