  We update the indirect bounds on anomalous triple gauge couplings coming from
the non-universal one-loop contributions to the $Z \to b \bar{b}$ width. These
bounds, which are independent of the Higgs boson mass, are in agreement with
the standard model predictions for the gauge boson self-couplings since the
present value of $R_b$ agrees fairly well with the theoretical estimates.
Moreover, these indirect constraints on $\Delta g^Z_1$ and $g^Z_5$ are more
stringent than the present direct bounds on these quantities, while the
indirect limit on $\lambda_Z$ is weaker than the available experimental data.
