A method of manufacturing a fixed type constant velocity universal joint, the fixed type constant velocity universal joint comprising: an outer joint member having a cup-like shape so as to open at one end and having an inner spherical surface provided with a plurality of track grooves extending in an axial direction; an inner joint member having an outer spherical surface provided with a plurality of track grooves extending in the axial direction in pairs with the plurality of track grooves of the outer joint member; a plurality of balls interposed between the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member so as to transmit torque; and a cage interposed between the inner spherical surface of the outer joint member and the outer spherical surface of the inner joint member so as to hold the plurality of balls, at least one of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member being formed by cold-forging finishing, characterized by the steps of ranking, without ranking of outer joint members and inner joint members according to a PCD according to outer diameters of the plurality of balls, cages having pocket widths in conformity with the outer diameters of the plurality of balls; measuring a PCD of the outer joint member, which has been arbitrarily selected, and a PCD of the inner joint member, which has been arbitrarily selected; and combining components comprising the outer joint member, the inner joint member, the plurality of balls, and the cage with each other based on matching in which the plurality of balls and the cage each having a rank corresponding to a measured value of the PCD of the arbitrarily selected outer joint member and to a measured value of the PCD of the arbitrarily selected inner joint member are selected with respect to the arbitrarily selected outer joint member and the arbitrarily selected inner joint member, forming cutout round portions (12a,22a) at least at one of an opening end of each of the plurality of track grooves of the outer joint member and one opening end of each of the plurality of track grooves of the inner joint member at least at parts corresponding to ball-contact points (P,Q), wherein the plurality of track grooves and the cutout round portions of the outer joint member are formed by simultaneous cold-forging finishing an outer joint member having a cup-like shape so as to open at one end and having an inner spherical surface provided with a plurality of track grooves extending in an axial direction; an inner joint member having an outer spherical surface provided with a plurality of track grooves extending in the axial direction in pairs with the plurality of track grooves of the outer joint member; a plurality of balls interposed between the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member so as to transmit torque; and a cage interposed between the inner spherical surface of the outer joint member and the outer spherical surface of the inner joint member so as to hold the plurality of balls, at least one of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member being formed by cold-forging finishing, characterized by the steps of ranking, without ranking of outer joint members and inner joint members according to a PCD according to outer diameters of the plurality of balls, cages having pocket widths in conformity with the outer diameters of the plurality of balls; measuring a PCD of the outer joint member, which has been arbitrarily selected, and a PCD of the inner joint member, which has been arbitrarily selected; and combining components comprising the outer joint member, the inner joint member, the plurality of balls, and the cage with each other based on matching in which the plurality of balls and the cage each having a rank corresponding to a measured value of the PCD of the arbitrarily selected outer joint member and to a measured value of the PCD of the arbitrarily selected inner joint member are selected with respect to the arbitrarily selected outer joint member and the arbitrarily selected inner joint member, forming cutout round portions (12a,22a) at least at one of an opening end of each of the plurality of track grooves of the outer joint member and one opening end of each of the plurality of track grooves of the inner joint member at least at parts corresponding to ball-contact points (P,Q), wherein the plurality of track grooves and the cutout round portions of the outer joint member are formed by simultaneous cold-forging finishing