  We study the effect of R**2 term to the modulated instability in the U(1)
charged black hole in five-dimensional Anti-de Sitter space-time. We consider
the first-order corrections of R**2 term to the background and the linear order
perturbations in the equations of motion. From the analysis, we clarify the
effect of R**2 term in the modulated instability, and conclude that
fluctuations are stable in the whole bulk in the range of values the
coefficient of R**2 term can take.
