Based on the density functional theory and crystal structure prediction approaches, we found a novel high-pressure structure of Fe2CO4-P1¯. It is characterized by the presence of ethane-like O3C–CO3 groups or so-called orthooxalate groups. The formation of such O3C–CO3 groups has been proposed earlier in melts and aqueous carbonate solutions, but no such examples were known in inorganic crystalline materials. We found that this structure is dynamically and thermally stable at pressures of 50 GPa. Similar structures were also predicted to be dynamically stable for Mn2CO4, Ni2CO4, and Co2CO4. In addition, FeCO3 was found to transform into a similar structure with O3C–CO3 orthooxalate groups at a pressure above 275 GPa. Additionally, for the first time, we describe the self-diffusion of metal atoms in carbonates at high pressure and at high temperatures. The prediction of novel carbonate structures extends the crystal chemistry of inorganic carbonates beyond the established ones with [CO3] triangles, [C2O5] pyro-groups, and [CO4] tetrahedra.