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This study starts with a question on two related, unverified assumptions about the cognitive or psychological concept of coherence in discourse: the definition of textual coherence is so abstract and varied that it may be rated differently by language users with different language backgrounds, and that it does not explicitly reveal its overall shape on the surface of text. We conduct an experiment with three stages on 33 argumentative essays written by native and non-native speakers of English: ratings of coherence, distribution and organization of coherence proper Linking Adverbials (LAs). The results show that there is quite a consistent pattern in 10 international raters’ assessment on textual coherence of the essays. The difference in the pattern of arranging coherence proper LAs between the high and low group reveals the optimal arrangement of coherence proper LAs, which is assumed to work to the effect that maximizes the cognitive concept of coherence.