  Model-independent search for the Abelian $Z'$ gauge boson virtual state based
on the new observable in the processes $e^+ e^- \to l^+ l^-$ is analyzed for
the LEP data. The observable is introduced by using following from
renormalizability of an underlying theory the correlations between the
parameters of the low energy effective Lagrangian and kinematics of the
scattering processes. The central values of the observable are in accordance
with the $Z'$ existence, although no real signal is found at the $1\sigma$
level. Lower limits at the 95% confidence level on the corresponding contact
interaction scale are derived in the range of 15.6 - 18.6 TeV. Comparisons with
other fits are done.
