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We propose a divide-and-conquer algorithm to find recursively the Scattering matrix of general tight-binding structures. The Scattering matrix allows a direct calculation of transport properties in mesoscopic systems by using the Landauer formula. The method is exact, and by analyzing the performance of the algorithm in square, triangular and honeycomb lattices, we show a significant improvement in comparison to other state-of-the-art recursive and non-recursive methods. We utilize this algorithm to compute the conductance of a rotated graphene nanoribbon side-contact junction, revealing that for electrons with energies smaller than -2.7eV the transmission function depends negligibly on the angle of the junction, whereas for electrons with energies greater than -2.7eV, there exists a set of angles for the system that increase its conductance independently of the energy of the particles.