We use density functional theory (DFT) calculations to investigate structural models consisting of anatase $\mathrm{Ti}{\mathrm{O}}_{2}\left(101\right)$ slabs covered by reduced overlayers formed by (101) crystallographic shear planes (CSPs). Ab initio thermodynamics supports the stability of these structures under a wide range of experimental conditions. The overlayers are found to have $\mathrm{T}{\mathrm{i}}_{2}{\mathrm{O}}_{3}$ stoichiometry with a crystal structure different from the known corundumlike $\mathrm{T}{\mathrm{i}}_{2}{\mathrm{O}}_{3}$ (here denoted a $\alpha \text{−}\mathrm{T}{\mathrm{i}}_{2}{\mathrm{O}}_{3}$) phase. DFT calculations predict this new “$\mathrm{csp}\text{−}\mathrm{T}{\mathrm{i}}_{2}{\mathrm{O}}_{3}$” phase to be energetically close to $\alpha \text{−}\mathrm{T}{\mathrm{i}}_{2}{\mathrm{O}}_{3}$ and to have also a similar band gap. These results suggest a possible role of the $\mathrm{csp}\text{−}\mathrm{T}{\mathrm{i}}_{2}{\mathrm{O}}_{3}$ phase in the properties of black $\mathrm{Ti}{\mathrm{O}}_{2}$, a promising photocatalytic material made of nanoparticles with a crystalline $\mathrm{Ti}{\mathrm{O}}_{2}$ core and a highly reduced $\mathrm{Ti}{\mathrm{O}}_{x}$ shell that is capable of absorbing the whole spectrum of visible light.