  The heavy Z' boson with family nonuniversal couplings can introduce flavour
changing effects. Constraints on nondiagonal Z' couplings coming from the \mu-e
conversion in a muonic atom, K^0 - \bar{K^0} and B - \bar{B} mixing, epsilon
and epsilon'/ \epsilon CP- violating coefficients have been already
established. By using the OPAL upper bound of the branching ratio for the B^-
-> K^- K^- \pi^+ decay, we indicate additional constraints on the Z' couplings.
We comment also on the constraints of Z' couplings coming from the b->d d
\bar{s} transition. The constraint obtained here from the upper bound of the
B^- -> K^- K^- \pi^+ decay involves a different combination of couplings than
those previously presented, but is much weaker.
