This paper aims at investigating and identifying the factor that has led the back and forth relationship between China and the United States since 1989. Previous studies on this subject addressed the issue by taking either of two approaches: one with the micro view that interprets the back and forth relationship in the context of the end of the Cold war, on other hand, with the macro view that interprets the fragile relationship in the context of the rise of China. However, neither of the approaches explains with sufficiency the question at hand. Hence for the inquiry, this article suggests a fresh view by exploring alternative method of using a cognitive map of each nation`s leader, Jiangzemin and Bill Clinton. This article provides an empirical analysis through the Selected works of Jiangzemin and the speeches of Bill Clinton in 1998 for the first time in the field of Sino-US relationship studies in Korea. With the results of the cognitive map analysis, we can reach the following four points. Firstly, indicators of the forth relationship between China and the US are: i) the recognition by Bill Clinton on the importance of China`s economic growth and; ii) the US`s cooperation of science technology with China. Second, the conflict between China and the US results from the discordance of opinions on the matter of human rights and military power. Second, the conflict will inevitably arise on environmental issues around the globe including a global warming. Third, while China has yet to find a legitimate reason to agree upon these issues with the US, the US urges China of its cooperation. Lastly, Both China and the US attach great importance to the alliance with Japan. This implicates that relatively, issues involving Japan take more control in the China-US relationship, than those of Korea Peninsula.