  We present an extension of the Randall--Sundrum model in which, due to
spontaneous Lorentz symmetry breaking, graviton mixes with bulk vector fields
and becomes quasilocalized. The masses of KK modes comprising the
four-dimensional graviton are naturally exponentially small. This allows to
push the Lorentz breaking scale to as high as a few tenth of the Planck mass.
The model does not contain ghosts or tachyons and does not exhibit the van
Dam--Veltman--Zakharov discontinuity. The gravitational attraction between
static point masses becomes gradually weaker with increasing of separation and
gets replaced by repulsion (antigravity) at exponentially large distances.
