  We construct the effective action of a $D_p$-brane-anti-$D_p$-brane system by
making use of the non-abelian extension of tachyonic DBI action. We succeed the
construction by restricting the Chan-Paton factors of two non-BPS $D_p$-branes
in the action to the Chan-Paton factors of a $D_p\bar{D}_p$ system. For the
special case that both branes are coincident, the action reduces to the one
proposed by A. Sen. \\The effective $D_p\bar{D}_p$ potential indicates that
when branes separation is larger than the string length scale, there are two
minima in the tachyon direction. As branes move toward each other under the
gravitational force, the tachyon tunneling from false to true vacuum may make a
bubble formation followed by a classical evolution of the bubble. On the other
hand, when branes separation is smaller than the string length scale, the
potential shows one maximum and one minimum. In this case, a homogeneous
tachyon rolling in real time makes an attractive potential for the branes
distance. This classical force is speculated to be the effective force between
the two branes.
