A method and apparatus for separating multiple food pieces and removing clumps from food pieces in order to process individual pieces for subsequent packaging includes a vibrating conveyor bed which receives a substantially continuous supply of a dried product, such as RTE cereal or another snack product, and delivers the dried product to a screen unit including a plurality of spaced slots through which only individual food pieces can pass for further processing. Prior to the screen unit, the bed can be provided with an upstanding deflector member which diverts the traveling food product away from a discharge chute and onto the screen unit. In any case, the screen unit includes an upwardly angling portion, extending away from the discharge chute, for retaining product which needs to be further processed, while the discharge chute also has an associated, raised lip for product retention purposes.