A positioning system (20) for positioning a cone part of or for a CRT comprises a first and a second positioning means (22, 23) at positions corresponding to two corners of a side of a rectangle, and a third positioning means (21) at a position in the middle of the opposite side. The first and second means (22, 23) have a saddle-shaped contact surface, which is convex in the direction (51) from the tapered end to the wide end and concave (radius of curvature R) towards a central part of the rectangle, a contact surface of the third positioning means (21) is convex in the direction (51) from the tapered end to the wide end and convex or flat in a plane through the contact surfaces of the positioning means.