Remove any loose pieces of concrete from the corner by hand. Brush the crumbling corner with a stiff wire brush to remove debris. Brush until you hit firm concrete.
Insert a masonry drill bit into a power drill. Drill pilot holes into the center and corners of the damage 1-1/2 to 2 inches deep at a 45-degree angle.
Sink masonry screws into the pilot holes with a power drill so they do not protrude above the existing masonry. Test the depth of the screws by laying a flat board over the existing masonry surface and hanging it over the damage. If the screws touch or are within 1/4-inch of the board, sink them deeper. The screws will act as reinforcement and a gripping surface for the concrete patch.
Clean the corner to remove all dust, using a broom or shop vacuum.
Position a level board on its edge next to the crumbling corner and one along the front to create a corner form. Use boards tall enough to reach the height of the existing masonry or slightly surpass it. Hammer nails through the front board to secure it to the board running along the side. Place bricks next to and in front of the form to hold it in place.
Mix dry concrete mix with water in a bucket according to the manufacturer's instructions.
Paint on a coating of a masonry-bonding agent with a paintbrush over the damaged corner and screws.
Pick up wet concrete with a trowel and fill in the damaged corner. Pack the concrete in tightly and up to the same height as the existing concrete. Smooth the surface with a masonry edger. Let the concrete to set for one to two hours before you remove the form.