Final chlorine dioxide bleaching of lignocellulosic materials is most effective at a near-neutral pH but present industrial practice typically targets a final pH of between 3.5 and 4.0 because of the difficulty in achieving and maintaining near-neutral pH cost effectively. The in situ formation of bicarbonate before the addition of chlorine dioxide provides a way of maintaining the required near-neutral pH. Near-neutral final chlorine dioxide bleaching also produces a bleached pulp that is in a state that responds more effectively to fluorescent whitening or optical brightening agents.