Introducing an extended Lie derivative along the dual of A, the 3-form field of D = 11 supergravity, the full diffeomorphism algebra of D = 11 supergravity is presented. This algebra suggests a new formulation of the theory, where the 3-form field A is replaced by bivector Bab, bispinor B??, and spinor-vector ?a? 1-forms. Only the bivector 1-form Bab is propagating, and carries the same degrees of freedom of the 3-form in the usual formulation, its curl D [?Bab ?] being related to the F??ab curl of the 3-form. The other 1-forms are auxiliary, and the transformation rules on all the fields close on the equations of motion of D = 11 supergravity. MSC 2010: 53Z05, 83F50.