We present two relativistic correction schemes to account for the relativistic effects on one-bond metal-ligand: couplings. On the basis of the Pauli Hamiltonian, the first method is a direct analogue to the nonrelativistic spin-spin coupling approach. In the second method, however, only the s-orbital contraction of the coupling metal atom is taken into account in computing the Fermi-contact contribution. These schemes are applied to the calculation of metal-ligand reduced coupling constants K-1(M-L) in some group 4 and 12 hyrides, alkyl complexes, and cyano complexes, as,well as some platinum ammine and platinum phosphine complexes. It is shown that the second approximate: method, a refined version of the "hydrogen-like" relativistic correction suggested by Pyykko, gives greater: improvement over the nonrelativistic values and agrees better with experiments. Finally, the connection between the trans influence and coupling constants is discussed in the context of some square-planar platinum complexes.