Аннотация:We consider 2D Hubbard clusters magnetism in the strong coupling regime. We show that the mean field approach does not provide sufficient results. Acting in assumption that the origin of unphysical predictions is the lack of local moment fluctuations, we develop the recently introduced Fluctuating Local Field scheme in the vicinity of atomic limit. Our numerical calculations show significant qualitative improvement of the results obtained within the mean field approach. We supply the discussion of the results with the perspectives for future quantitative improvements.