The reel (4') of the combine header of the invention comprises a rotatable central tube (10) with side members (15,16) attached to the tube and with intermediate members (17,18) arranged between the side members and tine bars (19) coupled to the side and intermediate members. The intermediate members (17,18) are coupled to a pivoting mechanism for positioning them at a slanted angle with respect to the central tube (10), the slanted position of the intermediate members being stationary relative to the frame of the header while the reel is rotating. The tine bars are pivotably connected to the intermediate members, so that the rotation of the reel generates a reciprocating motion of the tine bars in the axial direction of the reel when the intermediate members (17,18) are in a slanted position. This in turn generates a sideways motion of the tines (14) attached to the tine bars. The sideways motion enables the lifting up of fallen crops lying parallel to the driving direction of the harvester.