A method or process is provided for removing selenate from an ion-exchange or an adsorption media regenerant stream. The regenerant stream is processed in a nanofiltration membrane which produces a permeate and a reject stream containing the selenate. A reducing agent, such as iron, is mixed with the reject stream and this gives rise to an oxidation-reduction reaction that reduces the selenate to selenite. Thereafter, the method includes adsorbing the selenate onto an adsorbent, such as hydrous iron oxide. The adsorbent and adsorbed selenite is removed from the reject stream via a solids-liquid separation process.