  In this work, we study Lagrangian formulations for self-dual gauge theories,
also known as chiral $n$-form gauge theories, for $n = 2p$ in $D = 4p+2$
dimensional spacetime. Motivated by a recent formulation of M5-branes derived
from the BLG model, we generalize the earlier Lagrangian formulation based on a
decomposition of spacetime into $(D-1)$ dimensions plus a special dimension, to
construct Lagrangian formulations based on a generic decomposition of spacetime
into $D'$ and $D" = D - D'$ dimensions. Although the Lorentz symmetry is not
manifest, we prove that the action is invariant under modified Lorentz
transformations.
