We demonstrate that a real-space transfer-matrix method can be used to directly evaluate the complex and real band structures of superlattices. The transfer-matrix method avoids the introduction of a supercell in the band-structure calculations. As a prototype we have used the direct space, minimal-basis linear combination of Gaussian orbitals method to evaluate the Hamiltonian and overlap-matrix elements. Our results for strained (Si${)}_{\mathrm{n}}$/(Ge${)}_{\mathrm{n}}$ (001) superlattices (n=2\char21{}5) are presented. We find all the above superlattices to have indirect band gaps. In particular, for (Si${)}_{4}$/(Ge${)}_{4}$ the lowest direct transition is at 1.38 eV. The results are in good agreement with recent experimental measurements.