A continuous centrifuge (10) has a basket (30) with upper and lower basket portions (43, 44) separated by an intermediate slip portion (45). The lower basket portion (43) has an included angle of 40 50.degree., to separate "green" molasses from the sugar crystals, while the upper basket portion (44) has an included angle of 50 60.degree., to separate washed molasses from the sugar crystals. The inner faces of the walls of the basket portions (43, 44) have radial drainage grooves (46), closed at their lower ends and opens at their upper ends, to discharge the molasses.