We usually talk about rotations in the clockwise or counterclockwise direction. But if a rotation is just a function defined on the space, then it is all about points and their images, and there is no "direction" involved.
For example, consider the unique rotation about $(0,0)$ that sends the point $(1,0)$ to the point $(0,1)$ in the plane. Is it in the clockwise or the counterclockwise direction ?
We could say it's counterclockwise because it's a 90° turn, but we could also say it's clockwise because it's a -270° turn. The conclusion seems then that the rotation has no direction in itself.