On non-linear action of multiple M2-branes

A non-linear SO(8)$\mathit{SO}(8)$ 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 MIJK$M^{IJK}$. We argue that the action should contain terms with odd number of MIJL$M^{IJL}$ as well. We modify the action to include them.