  The observables useful for the model independent search for signals of the
abelian Z' in the processes e^+ e^- \to {\bar f}f are introduced. They are
based on the renormalization group relations between the Z' couplings to the
Standard Model particles developed recently and extend the variables suggested
by Osland, Pankov and Paver. The bounds on the values of the observables at the
center-of-mass energy \sqrt{s} = 500GeV are derived.
