  With initial and final particles on-shell, the anomalous weak-magnetic dipole
moments of b and c quarks are electroweak gauge invariant quantities of the
effective couplings Zb\bar{b} and Zc\bar{c}, respectively, and good candidates
to test the Standard Model and/or new physics. Here we present a complete
computation of these quantities within the Standard Model. We show that
decoupling properties with respect to heavy particles do take place in the weak
magnetic moment. The obtained values, a_b(M_Z^2)=(2.98-1.56i)x10^(-4) and
a_c(M_Z^2)=(-2.80+1.09i)x10^(-5) are dominated by one-gluon exchange diagrams.
The electroweak corrections are less than 1% of the total magnitude.
