Biuret is removed from biuret-containing aqueous urea solutions in a multi-cycle process which involves sequential (A) removal of biuret by contact with an anion exchanger and (B) regeneration of the anion exchanger, in which method, in one or more cycles, the anion exchanger regenerant comprises an aqueous solution of a strong base which has been employed to regenerate the anion exchanger in a previous cycle. This procedure allows for recycling, and thus reuse, of the strong base regenerant which results in significant economy. Methods are also provided in which (A) one or both of the aqueous urea solution and regenerant have a relatively low calcium equivalent content, (B) a substantially non-alkaline regenerant is employed either as the only regenerant in one or more cycles or as a partial regenerant before regeneration with the strong base regenerant, (C) the carbonate content of one or more of the aqueous process streams is controlled and/or reduced, and/or (D) the concentration of biuret in the recycled strong base regenerant is periodically reduced. All of these factors contribute to process economy, anion exchanger life, and more efficient, less frequent regeneration.