  We present a new formulation to calculate the electric conductance of
mesoscopic conductors by utilizing the singular value decomposition, which is a
mathematical technique to manipulate matrices. Our formulation is useful in
treating conductors with rather complicated atomic structures, for which naive
recursion formula is cumbersome. It also has an advantage in scaling up the
calculation by using parallel computation, which potentially allows us the
real-scale calculations at the atomic level. On the other hands, the effects of
electron-electron interactions are hard to be treated within this framework,
since it depends crucially on the linearity of the system. In this paper, we
study graphene nanoribbons with external leads for a simple example.
