We present a relativistic formulation of the spin-spin coupling hyperfine terms based on the two component zeroth-order regular approximate Hamiltonian. The scalar relativistic parts of the resulting operators were used for an implementation into the Amsterdam density functional program. Application of the code for the calculation of one-bond metal-ligand couplings of systems containing W-183, Pt-195, Hg-199, and Pb-207 shows that scalar relativistic calculations are able to reproduce major parts of the relativistic effects on the coupling constants, which can be even larger in magnitude than the respective total nonrelativistic values. The spatial origin of the regular approximate relativistic analogue of the Fermi-contact contribution, which is usually responsible for the strong relativistic increase of the couplings, is analyzed. Its relativistic effects can be described by the relativistic increase of valence orbital density in the very vicinity of the heavy nucleus.