A new type of intermolecular bond, termed a blueshifting halogen bond, is found in the chlorotrifluoromethane-, bromotrifluoromethane-, chlorotrifluorosilicane-, and chlorodifluoroamine-related complexes. Counterpoise-corrected gradient optimization performed at a correlated ab initio level (MP2(full)/6-311++G(d,p)) shows a shortening of the C-Cl (C-Br, Si-Cl, or N-Cl) bond of the proton donor and a blueshifting of the corresponding C-Cl (C-Br, Si-Cl, or N-Cl) stretching frequency. In contrast to the conventional hydrogen bond and the blueshifting hydrogen bond, the topological and electronic properties and the origin of blueshifting halogen bond are also investigated.