  We show that the Gauss-Bonnet correction to Einstein gravity induces a
gravitational tachyon mode, namely an unstable spin 2 fluctuation, in the
Randall-Sundrum I model. We demonstrate that this instability is generically
related to the presence of a negative tension brane in the set-up, with or
without $Z_2$-symmetry across it. Indeed it is shown that the tachyon mode is a
bound state localised on any negative tension brane of co-dimension one,
embedded in anti-de Sitter background. We discuss the possible resolution of
this instability by the inclusion of induced gravity terms on the branes or by
an effective four-dimensional cosmological constant.
