  We present the general formulation of non-covariant Lagrangian of self-dual
gauge theory. After specifying the parameters therein the previous Lagrangian
in the decomposition of spacetime into $6=D_1+D_2$ and $6=D_1+D_2+D_3$ can be
obtained. The self-dual property of the general Lagrangian is proved in detail.
We furthermore show that the new non-covariant actions give field equations
with 6d Lorentz invariance. The method can be straightforward extended to any
dimension and we also give a short discussion about the 10D self-dual gauge
theory.
