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.

8 pages, to appear in PLB