Abstract: A grinding fixture provides for grinding a pair of oppositely positioned complementary ball engaging meridian race grooves in the external surface of the inner race member of a constant velocity universal joint, wherein the race grooves are characterized by offset centers. The fixture, adapted to receive and contain the inner race member for grinding, is engageable with, and rotatable between, headstock and tailstock members of a grinding machine. In a preferred embodiment, the fixture incorporates a slide assembly which is reciprocated between two offset parallel centerlines during grinding of a race member contained within the fixture.