Steps require more maintenance and repair than other concrete structures around the house because heavy use makes them more susceptible to damage. Horizontal surfaces on steps can be treated using the same products and techniques used on other masonry surfaces. For vertical surfaces, use quick-setting cement, and shape it to fit.
How to Replace a Step Corner
Retrieve the broken corner, then clean it and the mating surface with a wire brush. Apply latex bonding agent to both surfaces. If you do not have the broken piece, you can rebuild the corner with patching compound.
Spread a heavy layer of fortified patching compound on the surfaces to be joined, then press the broken piece into position. Lean a heavy brick or block against the repair until the patching compound sets (about 30 minutes) Cover the repair with plastic and protect it from traffic for at least one week.