Abstract: There is provide a shaft coupling of the type which can transmit power between two parallel shafts through rolling elements disposed at intersecting portions of guide grooves that intersect each other at a right angle which can always stably transmit power. Guide grooves 5 and 6 are formed in opposed surfaces of two plates 1 and 2 such that each adjacent pair of guide grooves formed in each of the plates extend in a direction that forms an angle of 45 degrees with a reference line X connecting the midpoint between their respective intersecting portions and the center of the plates. Elongated holes 7 are formed in the retainer 4 so that each elongated hole extends along a straight line connecting the two adjacent intersecting portions between the two adjacent pairs of opposed guide grooves. Each elongated hole 7 and two pairs of opposed guide grooves 5 and 6 form a pair of rolling element guide mechanisms.