  The Kondo-lattice model is well established as a method to describe an
exchange coupling between single conduction electrons and localized magnetic
moments. As a nontrivial exact result the zero-bandwidth limit (atomic limit)
can be used to test approximations for this model. As soon as the translational
symmetry is broken (for instance by sublattice structures) it is necessary to
consider more than one lattice site. Therefore, we study as a starting point
for generalizations the situation of a two-site cluster. An equation-of-motion
approach is chosen to obtain the one-particle Green's function. In order to
determine the spectral weights of its energy poles, we derive different
possibilities for the calculation of the involved correlation functions. In
this paper the analytical exact result for the situation of an insulator is
presented. In a forthcoming article we generalize the calculations to arbitrary
electron densities, keeping as the only constraint S=1/2.
