A bearing for use in a water pump or similar apparatus and a method of assembling the bearing. The bearing has a stepped shaft and a counterbored raceway at the fan or pulley end which allows for use of a larger number of balls in the raceway at the fan or pulley end, and which allows for using larger balls at the impeller end. The method of assembly of the bearing includes assembling balls and a cage to form a ball and cage assembly, assembling ball and cage assembly into the outer race at its pulley end, then sliding the shaft, impeller end first, into the outer race through the pulley end such that the first inner raceway and the first balls align with the first outer raceway. The shaft is then displaced in a direction perpendicular to its axial centerline within the outer race. A second plurality of balls is inserted onto the shaft within the outer race at its second outer raceway end, and a second cage is inserted over the shaft and within the outer race to surround the second plurality of balls.