  A novel efficient method to calculate the scattering matrix (SM) of arbitrary
tight-binding Hamiltonians is proposed, including cases with multiterminal
structures. In particular, the SM of two kind of fundamental structures are
given, which can be used to obtain the SM of bigger systems iteratively. Also,
a procedure to obtain the SM of layer-composed periodic leads is described.
This method allows renormalization approaches, which permits computations over
macroscopic length systems without introducing additional approximations.
Finally, the transmission coefficient of a ring-shaped multiterminal system and
the transmission function of a square-lattice nanoribbon with a reduced width
region are calculated.
