In this talk, we introduce the higher version of Adachi-Iyama-Reiten's support tau-tilting pairs, which are regarded as a generalization of maximal tau_n-rigid pairs in the sense of Jacobsen-Jorgensen. Assume that C is an (n+2)-angulated category with an n-suspension functor Sigma^n and T is an Opperman-Thomas cluster tilting object. We prove that relative n-rigid objects in C are in bijection with tau_n-rigid pairs in the n-abelian category C/add(Sigma^nT), and relative maximal n-rigid objects in C are in bijection with support tau_n-tilting pairs. We also prove that relative n-self-perpendicular objects are in bijection with maximal tau_n-rigid pairs. These results generalize work for C being 2n-Calabi-Yau by Jacobsen-Jorgensen and work for n=1 by Yang-Zhu. This is a joint work with Bin Zhu.