  We study an inhomogeneous decay of an unstable D-brane in the context of
Dirac-Born-Infeld~(DBI)-type effective action. We consider tachyon and
electromagnetic fields with dependence of time and one spatial coordinate, and
an exact solution is found under an exponentially decreasing tachyon potential,
$e^{-|T|/\sqrt{2}}$, which is valid for the description of the late time
behavior of an unstable D-brane. Though the obtained solution contains both
time and spatial dependence, the corresponding momentum density vanishes over
the entire spacetime region. The solution is governed by two parameters. One
adjusts the distribution of energy density in the inhomogeneous direction, and
the other interpolates between the homogeneous rolling tachyon and static
configuration. As time evolves, the energy of the unstable D-brane is converted
into the electric flux and tachyon matter.
