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We present a construction-by-correction approach to solve the obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) construction problem. We build an obstacle-weighted spanning tree as a guidance to construct OARSMT on an escape graph. We use Dijkstra's algorithm for routing. A refinement of U- shaped removal is applied during the routing process to further reduce the wire length. Our experimental results show that comparing to several state-of-the-art works this algorithm achieves the shortest average total wire length. It also uses short run time for practical-size problems.