Tape the parchment from the backside to the rim, following the curve of the wire, if the rip is at the rim. A horizontal tear away from the top or bottom rim of the lampshade can be patched by using masking tape to reattach it to the rim.
Cover the ripped area of the lampshade with masking tape, if it's not at the rim. You can cover either the outside or inside of the shade.
Cut pieces of craft paper, such as that used for scrapbooking, into strips or other shapes you like. There are a number of creative ways to apply the paper, so make a simple patch in the same color as your current shade, or redecorate the entire shade in a patchwork, stripe or other pattern you like.
Paint decoupage glue onto the back of the pieces of craft paper or replacement parchment paper.
Glue the pieces of paper to the lampshade, beginning at the ripped area. Cover the entire shade with the paper pieces, or just make a patch.
Paint the entire shade with decoupage glue after you apply all the paper pieces. This creates a protective coating over the paper, prevents further rips, and makes the paper pieces meld together as one piece. The glue dries clear.