Conversations are often held in laboratories and companies. A summary is vital to grasp the content of a discussion for people who did not attend the discussion. If the summary is illustrated as an argument structure, it is helpful to grasp the discussion’s essentials immediately. Our purpose in this paper is to predict a link structure between nodes that consist of utterances in a conversation: classification of each node pair into “linked” or “not-linked.” One approach to predict the structure is to utilize machine learning models. However, the result tends to over-generate links of nodes. To solve this problem, we introduce a two-step method to the structure prediction task. We utilize a machine learning-based approach as the first step: a link prediction task. Then, we apply a score-based approach as the second step: a link selection task. Our two-step methods dramatically improved the accuracy as compared with one-step methods based on SVM and BERT.