Purified water for special purposes is produced using a falling-film multieffect evaporator. From the feed water, each effect produces a steam phase and a water phase. The steam phase is used for heating in the subsequent evaporating step, whereby the steam phase condenses to product water, and the water phase becomes feed water for the subsequent evaporation step. According to the invention, theproduct water may be wholly or partly recycled to the initial feed water, allowing process startup and sterilisation of the plant without conducting hot product water to the drain.