  The Randall-Sundrum two-brane model admits the flat-brane Lorentz-invariant
vacuum solution only if the branes have exactly opposite tensions. We pay
attention to this condition and propose a generalization of this model in which
two branes are described by actions of the same form and with the same matter
content but {\em with opposite signs}. In this way, the relation between their
tensions (which are their vacuum energy densities) is naturally accounted for.
We study a simple example of such a model in detail. It represents the
Randall-Sundrum model supplemented by the Einstein scalar-curvature terms in
the actions for the branes. We show that this model is tachyon-free for
sufficiently large negative values of the brane cosmological constant, that
gravitational forces on the branes are of opposite signs, and that physically
most reasonable model of this type is the one where the five-dimensional
gravity is localized around the visible brane. The massive gravitational modes
in this model have ghost-like character, and we discuss the significance of
this fact for the quantum instability of the vacuum on the visible brane.
