Undercoordinated indium (In*) is found to be an intrinsic defect that acts as a strong electron trap in amorphous InGaZnO4. Conduction electrons couple with the under-coordinated In* via Coulomb attraction, which is the driving force for the formation of an In*-M (M=In, Ga, or Zn) bond. The new structure is stable in the electron-trapped (2-) charge state, and we designate it as an intrinsic (In*-M)(2-) center in amorphous InGaZnO4. The (In*-M)(2-) centers are preferentially formed in heavily n-doped samples, resulting in a doping limit. They are also formed by electrical/optical stresses, which generate excited electrons, resulting in a metastable change in their electrical properties.