PURPOSE: To economize material cost and improve productivity by forming a key piece by bending a ring body outwardly after punching out the key piece integrally with the ring body inside said ring body, in Oldham's coupling.

CONSTITUTION: In the manufacture of a key piece 30 which slides in the key way 29 on an edge plate 21 of an Oldham's coupling 27 for preventing rotation of a swirl scroll 15, the useless taking-in of material can be reduced by the integral punching-out with a ring body 28 inside said ring body 28. Then, the difference of height is formed from a key piece 32 which slides in a key way 31 on a frame 8 by bending the key piece 30 outwardly from the ring body 28, and the upper surface of the frame 8 is made so as to permit the revolution of the swirl scroll 15. Since the Oldham's coupling can be formed through press work, and the height difference can be formed on the key piece by only bending the key piece, material can be economized, and productivity can be improved.