We review the derivation of a 6d gauge theory related to the M5 brane from the Bagger-Lambert-Gustavsson (BLG) model with the volume preserving diffeomorphisms gauge group. In particular, the Lagrangian for the 6d self-dual antisymmetric tensor field appears upon converting three of eight scalars in the BLG theory into the components of antisymmetric tensor field in D=6. We develop also a Lorentz-covariant Lagrangian formulation for such an antisymmetric tensor field in the free case. This formulation admits a natural supersymmetrization as well as coupling to 6d gravity.