We study the possible rotation of cluster galaxies, developing, testing, and applying a novel algorithm which identifies rotation, if such does exist, as well as its rotational centre, its axis orientation, rotational velocity amplitude, and, finally, the clockwise or counterclockwise direction of rotation on the plane of the sky. To validate our algorithms we construct realistic Monte Carlo mock rotating clusters and confirm that our method provides robust indications of rotation. We then apply our methodology on a sample of Abell clusters with z=50)

Cone search capability for table J/MNRAS/465/2616/table5 (*The clusters with significant rotation within r=2.5h^-1^_70_Mpc and with Nmem>=50)