The present computational study describes the structure and properties of a substoichiometric 2D monatomic in the height phase of nickel oxide, c(4 x 2)-Ni3O4, which has been newly found to epitaxially grow under special deposition conditions on the (100) face of palladium. A slab model is adopted where palladium is simulated by a thin film covered on both sides by epilayers, in combination with a DFT hybrid-exchange Hamiltonian; to make convergence of the SCF procedure easier, a thermal smearing technique is used, whose consequences on the results are critically analyzed. Three adsorbed systems are considered and characterized: (i) RH, that is, the c(4 x 2)-Ni3O4 phase with a rhombic distribution of Ni vacancies, as is experimentally observed; SQ, or p(2 x 2)-Ni3O4, which differs from the previous one for a square, instead of a rhombic distribution of vacancies; (iii) OX, or p(2 x 2)-O, that is, a surface oxidized phase of Pd(100) which is believed to be the precursor for the formation of RH. For a better understanding of the interaction of the metal with the adlayers, the isolated substoichiometric oxides, i-RH and i-SQ, have also been studied. It is shown that RH is more stable than SQ by a few tenths of electronvolts per Ni3O4 unit, which justifies its preferential formation and that the surface reaction, OX + 3NiO(ads)-> RH, is thermodynamically possible. Special attention has been devoted to characterize RH from an energetic, geometric. electronic, and magnetic viewpoint. The strong bond which is formed between surface Pd and O ions in the adlayer is responsible for some peculiar aspects of the electronic and magnetic structures of that phase.