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Orthogonal range search is ubiquitous nowadays, with natural applications in databases, data mining, and text indexing. Very recently, yet another application was discovered, which is to maintain a DFS forest in a dynamic graph. In this paper, we want to extend the above recent study, by applying orthogonal range search to efficient maintenance of a BFS-like forest, called no-back-edge-traversal (NBET) forest, which refers to a spanning forest obtained from a traversal that does not create any back edge. The study of such a problem is motivated by the fact that NBET forest can be used as a strong certificate of 2-connectivity of an undirected graph, which is more general than a spanning forest obtained from a scan-first search traversal.