  We present a time-dependent solution of the Nambu-Goto action which
represents two colliding waves moving at the speed of light. This solution can
be decomposed into two distinct regions with different geometries corresponding
to shrinking or expanding brane universe and two colliding branes. The former
describes the Big Bounce without singularity while the latter describes that
two branes collide and reconnect to each other. The colliding brane region has
a signature change. Classical dynamics of a massive particle on the brane is
studied through the geodesics.
