  We introduce the Korringa-Kohn-Rostocker non-local coherent potential
approximation (KKR-NLCPA) for describing the electronic structure of disordered
systems. The KKR-NLCPA systematically provides a hierarchy of improvements upon
the widely used KKR-CPA approach and includes non-local correlations in the
disorder configurations by means of a self-consistently embedded cluster. The
KKR-NLCPA method satisfies all of the requirements for a successful cluster
generalization of the KKR-CPA; it remains fully causal, becomes exact in the
limit of large cluster sizes, reduces to the KKR-CPA for a single-site cluster,
is straightforward to implement numerically, and enables the effects of
short-range order upon the electronic structure to be investigated. In
particular, it is suitable for combination with electronic density functional
theory to give an ab-initio description of disordered systems. Future
applications to charge correlation and lattice displacement effects in alloys
and spin fluctuations in magnets amongst others are very promising. We
illustrate the method by application to a simple one-dimensional model.
