  In this paper, we establish the super Poincar\'e inequality for the
two-parameter Dirichlet process when the partition number of the state space is
finite. Furthermore, if the partition number is infinite, the super Poincar'e
inequality doesn't hold. To overcome the difficulty caused by the degenerency
of the diffusion coefficient on the boundary of the domain, localization method
and perturbation argument in [14] are effective.
