The role of mutual atomic replacements in the formation of the energy, spectral and spin characteristics of the CoTiSb alloy is explored using the band structure calculations within the LAPW approximation. As found, the ground state (with the largest cohesive energy) is realized in the case of the arrangement of cobalt atoms in the crystallographic positions ($4с$) with tetrahedral atomic surroundings, and their replacement with titanium or antimony contributes to the energy of highly metastable phases. As revealed, the interchangement between the atomic positions, which form sublattice of NaCl type, does not lead to changes in the energy characteristics and the electronic structure of the CoTiSb alloy; the ground state is a nonmagnetic insulator, the metastable phases are converted into metallic ones with spin-polarized electron states and the ferrimagnetic type ordering of the magnetic moments of the atoms in cobalt and titanium sublattices.