Lots of search results on the Internet tell you how to remove an old door knob. None of them tells you how to proceed after you remove the knob itself, then the circular decorative cover and you are left with a second, thicker cover, with 2 holes but no screws:
What I think your describing is like a commercial knob. ( no pic) once you remove the knob and cover,the thicker ring twists off like a screw.there are no screws that hold that type of knob together I believe.
Most likely there is a slot somewhere on the sheath that has to be depressed in order for the knob to be separated. At home, a finger nail file tip is a good item to push into the slot. Wiggle the nob while pressing into the slot and you'll usually get some separation. Otherwise, it's possible the face plate (item with the two screw holes) could come off to reveal additional screws.