The multiplicative Ienormalization gloup (~) was first used in critical phenomena to discuss the homogeneity property of the order parameter-order parameter correlation function (2). Under the assumption of the asymptotic regularity of a certain function, followlug GELL-MANN and Low, the approach was then extended (a) to include an explicit equation for the coherence distance as well as a microscopic definition of the critical indices 7, v and ~. For simplicity in all these cases, where no at tempt at the evaluation of critical indices was made, only the wave function renormalization was considered. The severe restrictions necessary to obtain the Kadanoff apploach (4) to scaling from the group equations and the connection between these last equations and the Migdal (~) renormalized Ward identities were also discussed (a). WILSO~ (6) started by giving a more rigorous basis for the. Kadanoff cell model. He then generalized his procedure extending his analysis to cells in phase-space. Starting from an effective interaction of the Landau-Ginzburg type, he constructed a reeulrence relation for it. The name renormalization group in this context specifies the group of transformations which iterate the effective interaction. Noting that the recurrence relation, which is only approximate in three dimensions, turns out to be exact in four dimensions, recently WILSO~ himself and several other authors (7) have used it to cal-