  We consider flat solutions in the brane background with a massless scalar
field appearing in 5D $H^2_{MNPQ}$. Since there exist bulk singularities or
arises the divergent 4D Planck mass, we should introduce a compact extra
dimension, the size of which is then fixed by brane tension(s) and a bulk
cosmological constant. Inspecting scalar perturbations around the flat
solutions, we find that the flat solutions are stable vacua from the positive
mass spectrum of radion. We show that the massless radion mode is projected out
by the boundary condition arising in cutting off the extra dimension. Thus, the
fixed extra dimension is not alterable, which is not useful toward a
self-tuning of the cosmological constant.
