  Introducing an extended Lie derivative along the dual of A, the three-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 three-form field A is replaced by bivector B^{ab}, bispinor
B^{\alpha\beta}, and spinor-vector \eta^{a\beta} one-forms. Only the bivector
one-form B^{ab} is propagating, and carries the same degrees of freedom of the
three-form in the usual formulation, its curl \Dcal_{[\mu} B^{ab}_{\nu]} being
related to the F_{\mu \nu a b} curl of the three-form. The other one-forms are
auxiliary, and the transformation rules on all the fields close on the
equations of motion of d=11 supergravity.
