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The Steiner minimum tree (SMT) problem is one of the classic nonlinear combinatorial optimization problems for centuries. A novel solution, longest side elimination solution method (LSEM), is proposed in this paper. Firstly, the minimum spanning trees is defined as convex road and external side. Secondly, LSESM is constructed for solving the full SMT by using Melzak geometric composition principle to choose several points convex road which can satisfied certain conditions in the minimum spanning tree. And lastly, we can construct point set's full SMT according to visualization experiment results and Melzak geometric composition principle, combining with LSEM. A subsection-inserting points algorithm (SIPA) is described for eliminating the longest side in the convex road and solving the system shortest path sequentially. The global shortest path can be obtained by SIPA successfully compared with experimental results of visualization instrument.