The structural behaviors of IrTi are studied using first-principles density-functional theory with pseudopotentials and a plane-wave basis. Phonon calculations indicate that the tetragonal (L10) structure is dynamically unstable. We obtain the orthorhombic structure (Cmmm) which is shown to be a global energy minimum by the frozen phonon method. The resulting structure is mechanically and dynamically stable and its lattice constant is similar to the experimentally observed lattice constant of low-temperature structure, which demonstrates that the low-temperature phase of IrTi is the orthorhombic structure (Cmmm). Thus, we put an end to the experimental debate regarding the low-temperature phase: whether it is orthorhombic or monoclinic, and demonstrate theoretically that the IrTi alloys will undergo a cubic→tetragonal→orthorhombic transformation.