On non-linear action of multiple M2-branes

A nonlinear SO(8) invariant BF type Lagrangian for describing the dynamics of N M2-branes in flat spacetime has been proposed recently in the literature which is an extension of the non-abelian DBI action of N D2-branes. This action includes only terms with even number of the totally antisymmetric tensor M^{IJK}. We argue that the action should contain terms with odd number of M^{IJL} as well. We modify the action to include them.