The phylogeny reconstruction problem is a fundamental problem in computational molecular biology and biochemical physics. Since the number of data sets has grown substantially in recent years, the accuracy and speed of constructing phylogenies become increasingly critical. Numerous studies have demonstrated that the maximum likelihood (ML) method is the most effective method for reconstructing a phylogenetic tree from sequence data. Conversely, tree bisection and reconnection (TBR) is a tree topology rearrangement method that can generate an extensive tree space. In this paper, we propose an enhanced method for reconstructing phylogenetic trees in which the TBR operation is modified and combined with the minimum evolution principle to filter out some unnecessary reconnected positions to reduce the search time. The experiment results demonstrate that the proposed method can assist other algorithms in constructing more accurate trees within a reasonable time.