A method of enhancing the dewatering of a paper sheet on a paper machine comprising adding to the paper sheet about 0.05 lb/ton to about 15 lb/ton, based on dry fiber, of one or more aldehyde functionalized polymers comprising amino or amido groups wherein at least about 15 mole percent of the amino or amido groups are functionalized by reacting with one or more aldehydes and wherein the aldehyde functionalized polymers have a molecular weight of at least about 100,000.