Sodium-ion batteries offer a potential solution to the problem of limited lithium resources, and the newly developed positive electrode material Na4Co3(PO4)2P2O7 is attracting significant attention due to its high rate, high capacity, and high voltage compared to other sodium-ion battery materials. However, details of its electronic structure and its charge/discharge behavior are still uncertain. Here we report detailed first-principles calculations of the desodiation behavior of Na4Co3(PO4)2P2O7 using the GGA + U formalism of density functional theory. Assuming a stepwise desodiation process, removal of Na down to NaCo3(PO4)2P2O7 is found to be accompanied by oxidation of Co2+ to Co3+. Further removal of Na to give Co3(PO4)2P2O7 requires oxidation of oxygen 2p orbitals in the P2O7 polyhedra instead of Co3+ being oxidized to Co4+. The holes thus formed are expected to be strongly self-trapped, rendering them immobile at room temperature. At the same time, a large volume shrinkage is observed during this last desodiation step, constricting the Na migration channels. These two factors may explain the difficulty encountered experimentally in removing all Na from Na4Co3(PO4)2P2O7.