Abstract: In this paper, the smallest weight spanning tree in the non-oriented complete graph, which is usually encountered in IC's routing, is discussed. An algorithm for finding the smallest weight spanning tree is presented. It is called the upper-triangular-matrix algorithm (briefly as M-algorithm). The data structure that supports the algorithm is described. For the complete graph G(n, e), the complexities in computing and in storage of the M-algorithm are 0(n³) and 0(n²), respectively. For the same storage requirements, the M-algorithm is superior to Kruskal's algorithm in computing.