At any time within six months from the date of rendition of the last judgment awarding compensation for any such improvement in the superior court, or if appellate review is sought, then within two months after the final determination of the proceeding in the supreme court or the court of appeals, any such city may discontinue the proceedings by ordinance passed for that purpose before making payment or proceeding with the improvement by paying or depositing in court all taxable costs incurred by any parties to the proceedings up to the time of such discontinuance. Except as provided in RCW
8.25.290(3), if any such improvement be discontinued, no new proceedings shall be undertaken therefor until the expiration of one year from the date of such discontinuance.