Summary: The \(R^h\)-restricted connectivity \(\kappa^h\) is a significant measurement to estimate the reliability of large-scale processor system. The arrangement graph \(A_{n,k}\) is a generalization and also a competitive alternative of the star graph \(S_n\). In this paper, for any non-negative integer \(h\leq n-2\), we determine that \(\kappa^h(A_{n,2})=n(n-2)/2\) provided \(h\) is odd with \(h=n-3\), otherwise \(\kappa^h(A_{n,2})=(h+2)(n-2)-\lfloor h^2/2+h\rfloor\). This result implies the upper bound of \(\kappa^h(A_{n,k})\) given by L. P. Li et al. [Int. J. Heat Mass Transfer 51, No. 13–14, 3669–3682 (2008; Zbl 1148.80327)] is not optimal in a sense.