How do you sharpen a corner chisel?

I use a spring-loaded corner chisel (below)—and a few mallet taps—to square up corners of hinge mortises and similar recesses. But how do I sharpen it after the cutting edge dulls?
—Jessica Petrey, Danielson, Conn.

Remove the plate that holds the chisel in its housing, Jessica, taking care to not lose the spring concealed inside the housing. Then use a diamond file (woodcraft, no. 852974, 800-535-4482, woodcraft.com) to hone the inside bevels of the 90° tip. Keep the file flat against the beveled edges and make about 10–20 strokes per side; repeat until sharp. When finished, make a couple of passes on the flat back side to remove any burr, and reinstall the plate.