A radiation therapy unit with a beam of rays propagating from a focal point along a beam axis comprises a radiator head arranged on the beam axis with a double-focus multi-leaf collimator. The multi-leaf collimator exhibits a plurality of adjacently arranged diaphragm plates which in each case have two side faces, two front faces and an inside and an outside face. Each side face of each diaphragm plate forms a part of a surface area of a cone, all such cones having both a common cone axis which extends perpendicularly to the beam axis through the focal point, and a common cone point which coincides with the focal point. Means are provided for guiding the diaphragm plates so that each diaphragm plate performs a pure rotation about the cone axis during its displacement.