  A new Lagrangian realizing the symmetry of the M Algebra in
eleven-dimensional space-time is presented. By means of the novel technique of
Abelian Semigroup Expansion, a link between the M Algebra and the
orthosymplectic algebra osp(32|1) is established, and an M Algebra-invariant
symmetric tensor of rank six is computed. This symmetric invariant tensor is a
key ingredient in the construction of the new Lagrangian. The gauge-invariant
Lagrangian is displayed in an explicitly Lorentz-invariant way by means of a
subspace separation method based on the extended Cartan homotopy formula.
