The invention relates to a method of producing a bright, yeast fermented beverage, said method comprising the continuous production of wort from mash. More particularly, the present method comprises: a. mashing in a particulate, starch-containing raw material with water and enzymatically hydrolysing the starch to fermentable sugars; b. continuously producing a fermentable wort from the heated mash; c. introducing the wort into a fermenter to ferment the wort with the help of biologically active yeast; d. removing yeast from the fermentate by means of sedimentation; and e. clarifying the low-yeast fermentate to produce a bright, yeast fermented beverage by: processing the low-yeast fermentate in one or more separators to remove suspended material, said one or more separators being selected from the group consisting of centrifuges and decanter centrifuges; and filtering the processed fermentate. The efficiency with which the low-yeast fermentate is clarified to a bright beverage can be maintained during a very long period of time (e.g. for several weeks), which is particularly beneficial in case of a continuous brewing operation in which both wort production and yeast fermentation are carried out in a continuous fashion.