A cellular version of dynamical mean field theory (DMFT) which gives a natural generalization of its original single-site construction was analyzed using coherent potential approximation (CPA) technique. The solution of the cluster embedded in a medium results in a cluster Green's function matrix and a cluster self-energy matrix. The effective action for the cluster degrees of freedom was obtained by integrating all the variables in a path integral. The results show that DMFT produces information on problems where physics is local while the cluster methods is useful for the problems where correlations between more sites and orbitals are taken into account.