We present a new method to study the electronic density of states of an amorphous system of atoms with four‐fold coordination in terms of the local density of states of an atom in a small cluster of this system. Our results show unequivocally that thenumberandtypeof rings of bonds in thevicinity ofandpassing througha certain atom are intimately related to the position and number of peaks in the local density of states of this atom. The method involves choosing a small cluster of atoms and using the Bethe lattice as a boundary condition.