With the rapid application development for wireless sensor networks, effective information collection methods are becoming increasingly emphasized. The effectiveness of data aggregation is mainly determined by the routing structure while tree is an important structure for data aggregation. Many researchers have studied the problem of how to construct a routing tree in a wireless sensor network with relay nodes so that the total transmission and reception energy cost consumed by all sensors is minimized, the so-called Minimum Energy- Cost Aggregation Tree with Relay Nodes problem. In this paper, we propose an improved method to reconstruct a routing tree so that the total energy cost can be reduced. Using simulation, we demonstrate that a shortest path routing tree applied with our proposed Reconstruction algorithm could have lower total energy cost than the original one.