A connected graph is said to be super edge-connected if every minimum edge-cut isolates a vertex. The restricted edge-connectivity \(\lambda’\) of a connected graph is the minimum number of edges whose deletion results in a disconnected graph such that each component has at least two vertices. It has been shown by A. H. Esfahanian and S. L. Hakimi (On computing a conditional edge-connectivity of a graph. Information Processing Letters, 27(1988), 195-199] that \(\lambda'(G) \leq \xi(G)\) for any graph of order at least four that is not a star, where \(\xi(G) = \min\{d_G(u) + d_G(v) – 2: uv \text{ is an edge in } G\}\). A graph \(G\) is called \(\lambda’\)-optimal if \(\lambda'(G) = \xi(G)\). This paper proves that the de Bruijn undirected graph \(UB(d,n)\) is \(\lambda’\)-optimal except \(UB(2,1)\), \(UB(3,1)\), and \(UB(2,3)\), and hence, is super edge-connected for \(n\geq 1\) and \(d\geq 2\).