A stable complex, LiBr···BrF, is predicted in which the negative Br atom of LiBr is anchored to the Br atom of BrF by a halogen bond, while the positively charged Li atom interacts with the lone pair electron density on the Br atom of BrF in a direction roughly perpendicular to the halogen bond. As far as we are aware, this is the first reported instance of an atom of one diatomic molecule (Br of BrF) being bonded to two different, oppositely charged atoms (Li and Br) of another diatomic molecule (LiBr). Other less stable dimers of LiBr and BrF were predicted and compared with this novel complex.