A broccoli quartering machine for quartering spears of broccoli includes a conveyor adapted to move in a lineal path and having rigid plates upon which are mounted resilient, conical, cup-shaped holding members for holding the individual spears of broccoli. The apex of the cup-shaped members extends downward through an opening in each plate and is open, and each cup-shaped member includes at least two pairs of slots which extend from the open apex upward toward the base of the cup-shaped member. A plurality of cam followers are mounted on the cup-shaped members and contact a guide strip on the machine frame so as to align one pair of the slots with a first cutting disc and to engage a cam on the machine frame to rotate the cup-shaped member and the spear of broccoli therein 90.degree. between the first cutting disc and the second cutting disc so as to align the remaining pair of slots with the second cutting disc.