We report the first results of relativistic correlation calculation of the spectroscopic properties for the ground state of E112H and its cation in which spin-orbit interaction is taken into account non-perturbatively. Studying the properties of E112 (eka-Hg) is required for chemical identification of its long-lived isotope, 112283. It is shown that appropriate accounting for spin-orbit effects leads to dramatic impact on the properties of E112H whereas they are not so important for E112 H+. The calculated equilibrium distance, Recalc =1.662 Å, in E112H is notably smaller than Reexpt = (1.738±0.003) Å and Recalc =1.738 Å in HgH, whereas the dissociation energy, Decalc =0.42 eV, in E112H is close to Deexpt =0.46 eV and Decalc =0.41 eV in HgH. These data are quite different from Re NH =1.829 Å and De NH =0.06 eV obtained for E112H within the scalar-relativistic Douglas-Kroll approximation [Nakajima and Hirao, Chem. Phys. Lett. 329, 511 (2000)]. Our results indicate that E112 should not be expected to behave like a noble gas in contrast to the results by other authors.