  We consider a dynamical two-brane in a four dimensional black hole background
with scalar hair. At high temperature this black hole goes through a phase
transition by radiating away the scalar. The end phase is a topological
adS-Schwarzschild black hole. We argue here that for a sufficiently low
temperature, the brane motion in this geometry is non-singular. This results in
a universe which passes over from a contracting phase to an expanding one
without reaching a singularity.
