Organic light-emitting diodes (OLEDs) are among the most promising organic semiconductor devices. The recently reported external quantum efficiencies (EQEs) of 29-30% for green and blue phosphorescent OLEDs are considered to be near the limit for isotropically oriented iridium complexes. The preferred orientation of transition dipole moments has not been thoroughly considered for phosphorescent OLEDs because of the lack of an apparent driving force for a molecular arrangement in all but a few cases, even though horizontally oriented transition dipoles can result in efficiencies of over 30%. Here we use quantum chemical calculations to show that the preferred orientation of the transition dipole moments of heteroleptic iridium complexes (HICs) in OLEDs originates from the preferred direction of the HIC triplet transition dipole moments and the strong supramolecular arrangement within the co-host environment. We also demonstrate an unprecedentedly high EQE of 35.6% when using HICs with phosphorescent transition dipole moments oriented in the horizontal direction.