Put on your safety goggles and brush the concrete with the wire brush. Use the hammer and chisel to remove concrete beneath the area where it is crumbling. Work in an inverted "V" shape until you reach solid concrete. If loose concrete is not removed, the patch will break loose.
Make a concrete form from scrap lumber or new lumber, held together with screws. Build the form in an L-shape so you can patch one side at a time. Apply oil to the inside of the form so that it does not stick to the concrete. Hold the form in place against the first corner you intend to patch, using pieces of duct tape. Align the form with the top of the step or the patch will be uneven.
Apply the concrete bonding agent to the concrete, according to the directions. Mix a small amount of a quick-set concrete in a bucket, following the package directions. Use a trowel to apply the mix to the step. Push the mixture into the space and against the form. Overfill the corner section so the concrete is just above the top of the form. Use the trowel to smooth the mixture evenly.
Place plastic sheeting over the step to speed curing. The sheeting is optional, but concrete can crack if it dries too quickly and the plastic helps hold in the moisture. In any case, let the concrete set up overnight without walking on the steps. When it's dry, remove the plastic and the form.