We report new topological invariants in four dimensions that are generalizations of the Nieh-Yan topological invariant. The new topological invariants are obtained through a systematic method along the lines of the one used to get the Nieh-Yan form, but involving an S O (4, 1)[S O (5)] connection constructed out from an S O (3, 1)[S O (4)] connection and three S O (3, 1)[S O (4)] tensor 1-forms. We give explicit expressions of the new 4-forms that give rise to the new topological invariants for particular choices of these 1-forms and show that the Nieh-Yan form arises as a particular case.