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In this paper we present a rule-based stemming algorithm for the Uzbek language. Uzbek is an agglutinative language, so many words are formed by adding suffixes, and the number of suffixes is also large. For this reason, it is difficult to find a stem of words. The methodology is proposed for doing the stemming of the Uzbek words with an affix stripping approach whereas not including any database of the normal word forms of the Uzbek language. Word affixes are classified into fifteen classes and designed as finite state machines (FSMs) for each class according to morphological rules. We created fifteen FSMs and linked them together to create the Basic FSM. A lexicon of affixes in XML format was created and a stemming application for Uzbek words has been developed based on the FSMs., Comment: Preprint of the paper to be published at The International Conference and Workshop on Agglutinative Language Technologies as a challenge of Natural Language Processing (ALTNLP), June 6, 2022, Koper, Slovenia