  We investigate the relaxation rate of the RNdS black hole perturbed by
neutral massless scalar field in the eikonal limit. We find that the fastest
relaxation rate of the composed system increases with the cosmological constant
for all spacetime dimensions. We also find that, when the cosmological constant
decreases from maximum value to zero, the corresponding critical charge of the
four-dimensional RNdS black hole maximizing the relaxation rate of the composed
system gradually decreases monotonically to $\bar{Q}=0.726$. However, for the
higher dimensional systems, this is not the case and the critical charges
decrease from maximum to zero.
