The blocking step of the renormalization group method is usually carried out\nby restricting it to fluctuations and to local blocked action. The tree-level,\nbi-local saddle point contribution to the blocking, defined by the\ninfinitesimal decrease of the sharp cutoff in momentum space, is followed\nwithin the three dimensional Euclidean $\\phi^6$ model in this work. The phase\nstructure is changed, new phases and relevant operators are found and certain\nuniversality classes are restricted by the bi-local saddle …