This work deals with new classes of spinors of mass dimension 1 in Minkowski spacetime. In order to accomplish it, Lounesto’s classification scheme and the inversion theorem are going to be used. The algebraic framework shall be revisited by explicating the central point performed by the Fierz aggregate. Then the spinor classification is generalized in order to encompass the new mass dimension 1 spinors. The spinor operator is shown to play a prominent role to engender the new mass dimension 1 spinors, accordingly.