  A non-universal interaction associated with top quark induces flavor changing
neutral currents (FCNC) among light fermions. The size of the FCNC effect
depends crucially on the dynamics of the fermion mass generation. In this
paper, we study the effect of a non-universal interaction on $Z b b$, $Z b s$
{\it etc}, by using an effective lagrangian technique and assuming the quark
mass matrices in the form of a generalized Fritzsch ansatz. We point out that
if fitting $R_b$ to the LEP data within $1 \sigma$, the induced FCNC couplings
are very close to the experimental limits.
