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