  New equations governing the scale transformation behaviors of a QFT with
underlying structures are derived. These equations, with their several
equivalent versions, can yield some new and significant insights and results
that are difficult to see in the conventional renormalization programs. Among
the several equivalent versions, one is similar to the usual Callan-Symanzik
equation and renormalization group equation but with different meanings. From
another version, the anomalous equation of energy-momentum tensor trace can be
easily obtained. It can be shown that with the new versions one could partially
fix the scheme dependence and hence some renormalization schemes like momentum
space subtractions are questionable. The asymptotic freedom for QCD is easily
reproduced at one-loop level in our new version CSE. Finally the decoupling
theorem a la Appelquist and Carazzone are discussed within our strategy.
