A systematic study of the electronic state of a random lattice is made in this series of papers by making use of a Green's function method. As the first step, an exact method of averaging over a random distribution of impurities is given. With this strict averaging procedure, the one electron Green's function is determined in a self-consistent field approximation for a binary alloy. It is shown that the obtained Green's function has a dual symmetry which should be conserved in the exact Green's function.