A key assembly is press fit into an annular space between a box and pin member to resist relative rotation of the box and pin members. The key assembly includes wedge like members that contact one another along complementary tapered surfaces, and when in contact generate radial forces into the box and pin member to secure the connection between the box and pin. The outer wedge is inserted first into the annular space between the box and pin members, and has rows of elongate teeth that project radially outward into contact with an inner surface of the box member. Because the outer wedge is pushed radially outward against the box member rather than axially sliding therebetween, the teeth protrude into the surface of the box member thereby increasing the anti-rotation force created by the outer wedge.