Not exactly woodworking . . . sorry if this is OT

I'm trying to replace old (1970s) doorhandles. Trouble is, I can't see how
the old one comes off! I can unsnap the flange, but I don't see any screws
underneath. There are no hidden screws on the handle itself. It's a round
handle, the neck of which goes through the flange into the door. On the neck
of the handle there is a slot, but pushing a screwriver through the slot
does nothing.

Help. I'm almost at the "sledgehammer" stage

George