In this paper, we consider K-class classification problem, a significant issue in machine learning or artificial intelligence. in this problem, we are given a training set of samples, where each sample is represented by a nominal-valued vector and is labeled as one of the predefined K classes. The problem asks to construct a classifier that predicts the classes of future samples with high accuracy. For K = 2, we have studied a new visual classifier named 2-class SE-graph based classifier (2-SEC) in our previous works, which is constructed as follows: We first create several decision tables from the training set and extract a bipartite graph called an SE-graph that represents the relationship between the training set and the decision tables. We draw the SE-graph as a two-layered drawing by using an edge crossing minimization technique, and the resulting drawing acts as a visual classifier. We can extend 2-SEC to K-SEC for K > 2 naturally, but this extension does not consider the relationship between classes, and thus may perform badly on some data sets. In this paper, we propose SEC-TREE classifier for K > 2, which decomposes the given K-class problem into subproblems for fewer classes. Following our philosophy, we employ edge crossing minimization technique for this decomposition. Compared to previous decomposition strategies, SEC-TREE can extract any tree as the subproblem hierarchy. In computational studies, SEC-TREE outperforms C4.5 and is competitive with SVM especially when K is large.