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We extend the single-site coherent potential approximation (CPA) to includethe effects of non-local disorder correlations (alloy short-range order) on theelectronic structure of random alloy systems. This is achieved by mapping theoriginal Anderson disorder problem to that of a selfconsistently embeddedcluster. This cluster problem is then solved using the equations of motiontechnique. The CPA is recovered for cluster size $N_{c}=1$, and the disorderaveraged density-of-states (DOS) is always positive definite. Various newfeatures, compared to those observed in CPA, and related to repeated scatteringon pairs of sites, reflecting the effect of SRO are clearly visible in the DOS.It is explicitly shown that the cluster-CPA method always yieldspositive-definite DOS. Anderson localization effects have been investigatedwithin this approach. In general, we find that Anderson localization sets inbefore band splitting occurs, and that increasing partial order drives acontinuous transition from an Anderson insulator to an incoherent metal.Comment: 7 pages, 6 figures. submitted to PR

Cluster coherent potential approximation for the electronic structure of disordered alloys