Abstract: A heald or heddle frame for a high speed weaving machine comprises a side stay having a core made of metal, one portion of which is free to slide in a guiding groove of a device for guiding the heddle frame and the other portion of which is covered with plastic to provide additional strength, a pair of joining pieces projecting from the strengthened portion of the core of the side stay as one body and forming a tapered groove therebetween, a hollow cross beam of metal for receiving said joining pieces, and wedge means for pressing said joining pieces outwards being mounted in the tapered groove of the joining pieces.