An assembly for the frame of a switchboard is disclosed, which can include a hollow member which extends lengthwise along a reference axis and which has at least one slot. The assembly can include at least one connecting element for connecting the assembly to a corresponding corner joint element of the frame, and the connecting element can include an insulating body and a fixing metal plate which is associated to a carrying part of the insulating body. The carrying part can be at least partially inserted transversally with respect to the reference axis into the hollow member through the slot, so as to arrange at least a portion of the associated fixing metal plate into the hollow member transversally with respect to the reference axis.