A method I've heard of for getting over fear, and which sounds reasonable to me, is to slowly approach the fearful item. Don't let your fear level get too high, when it gets uncomfortable don't go closer. Get a bit closer each day so your subconscious learns that it is safe. You must do this yourself, if someone is forcing or pressuring you, it will only make the phobia worse.

And of course, make certain that it really is safe. You don't want to be getting closer and closer to a cornice that is likely to break under your weight, nor to any other dangerous edge.