  We construct an action for unstable M3-brane in M-theory. We argue that in
order to find M3-brane action that upon direct dimensional reduction leads to
non-BPS D3-brane action in type IIA theory we have to presume that the
background possesses Killing isometry and that this isometry has to be gauged
on the world-volume of M3-brane. Then we construct singular tachyon kink on
world-volume of M3-brane and we show that the dynamics of resulting topological
defect is governed by an action that upon direct dimensional reduction leads to
D2-brane in type IIA theory and that is equivalent to standard M2-brane action
in flat background.
