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This is how I did it. I went very slowly and first chipped away some of the outside shell. Wetting the membrane with warm (not hot) water as I went. I looked for any veins that still might have blood in them. If I didn't see any, then I would carefully breakaway the membrane from the chick (making sure that it was moist). I used sterile tweezers (and my fingers) as they were the easiest for me to use. I had to be very careful not to nick or pinch the chick. If I made a mistake and hit a vein that wasn't completely clear of blood then I stopped and put the chick back into the incubator for a while. Then I tried again.
Others have different methods, You will have to decide which is right for you.
Edited to add: Mine usually had been trying to hatch for so long that their veins were all dried up and I had no problems. I only had one chick that had a small amount of bleeding.
Now is the membrane your talking about the one that the shell is attatched to or the one that the chick is wrapped in?
The one the chick is wrapped in. That's the one with the veins (edited: I had to avoid the veins not the membrane.) that you have to avoid. When I helped my chicks, the membrane was tight around their little bodies and it was hard (sometimes) to find a place where (what ever implement you use to break it) I wouldn't be nicking the chick. The membrane around my little chicks was also very tough and hard to break. I also had to be careful not to squish them while trying to help them.
Added: I managed to help 6 chicks hatch and they are all healthy and doing well.