To improve the aesthetic qualities of door hardware, many modern-day manufacturers are producing doorknobs that come with a false cosmetic plate. This plate covers the operational hardware of the door handle, as well as the screws. The end-result is a more streamlined design, but until you know how the cosmetic plate is removed, it can be difficult to access the screws to remove the handle.
Examine the edge of the door handle's metal plate on the interior side of the door, looking for a hidden, recessed screw. This screw holds the plate in place, and it is usually sunk into the side of the plate, making it difficult to see at first glance.
Find an Allen wrench that fits the screw by trying each different size in the set until one fits. Insert the tip of the wrench into the screw, and rotate the tool counter-clockwise until the faceplate is free to slide off. Occasionally, the door handle may instead use a different screw type, such as a Phillip's head screw. If that is the case, use a screwdriver instead of an Allen wrench.
Slide the cosmetic faceplate away from the door. Depending on the door handle design, the faceplate may be able to slide completely off. If not, rotate the faceplate until the underlying screws are accessible, and use a Phillips-head screwdriver to remove them. The door handle will now slide off.