The periodic table provides a fundamental protocol for qualitatively classifying and predicting chemical properties based on periodicity. While the periodic law of chemical elements had already been rationalized within the framework of the nonrelativistic description of chemistry with quantum mechanics, this law was later known to be affected significantly by relativity. We here report a systematic theoretical study on the chemical bonding pattern change in the coinage metal dimers (Cu, Ag-2, Au-2, Rg(2)) due to the relativistic effect on the superheavy elements. Unlike the lighter congeners basically demonstrating ns ns bonding character and a O-g(+) ground state, Rg(2) shows unique 6d-6d bonding induced by strong relativity. Because of relativistic spin-orbit (SO) coupling effect in Rg, two nearly degenerate SO states, O-s(+) and 2(u), exist as candidate of the ground state. This relativity-induced change of bonding mechanism gives rise to various unique alteration of chemical properties compared with the lighter dimers, including higher intrinsic bond energy, force constant, and nuclear shielding. Our work thus provides a rather simple but clear-cut example, where the chemical bonding picture is significantly changed by relativistic effect, demonstrating the modified periodic law in heavy-element chemistry.