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This paper aims at finding out constraints on the center transition process in Korean narrative discourse to keep it the most coherent. For that purpose, I will analyze a Korean traditional story titled as ‘I-Sang-Han I-Pha-Ri (Magic Leaf)’ on the basis of Centering Theory which is originated from Grosz, Joshi & Weinstein (1995). In this approach, the interclausal anaphora resolution depends on those constraints. Firstly, I will introduce the algorithm of the Centering Theory with reference to Korean expressions. Secondly, I will present some working assumptions for the analysis of Korean utterances, which include the issues of recovering empty pronouns, dividing utterances, recognizing entities and arranging discourse segments. And then, I will discuss the analyzed results of the story to find out the constraints at issue including the forward- looking center ranking of Korean. Meanwhile, the global design of the story will be also considered