  We study the instability of a Reissner-Nordstr\"om-AdS (RNAdS) black hole
under perturbations of a massive scalar field coupled to Einstein tensor.
Calculating the potential of the scalar perturbations we find that as the
strength of the coupling of the scalar to Einstein tensor is increasing, the
potential develops a negative well outside the black hole horizon, indicating
an instability of the background RNAdS. We then investigate the effect of this
coupling on the quasinormal modes. We find that there exists a critical value
of the coupling which triggers the instability of the RNAdS. We also find that
as the charge of the RNAdS is increased towards its extremal value, the
critical value of the derivative coupling is decreased.
