De Sitter static black ring in large D membrane paradigm at the second order

It was shown in [1] that the effective stationary membrane equations from the large D membrane paradigm at the first order admit black ring solutions in flat and AdS cases, but the de Sitter solution obtained in [2] lies outside the domain of their applicability. In this short note the static de Sitter black ring is obtained from the second order membrane paradigm, and it satisfies the equilibrium condition for the thin ring solution of [2]. This provides a segue into the stationary black rings at the second order.