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This paper presents a method of using association rule data mining algorithms to discover regular sound changes among languages. The method presented has a great potential to facilitate linguistic studies aimed at identifying distantly related cognate languages. As an experimental example, this paper presents the application of the data mining method to the discovery of regular sound changes between the Hungarian and the Sumerian languages, which separated at least five thousand years ago when the Proto-Sumerian reached Mesopotamia. The data mining method discovered an important regular sound change between Hungarian word initial /f/ and Sumerian word initial /b/ phonemes.