2 breakers on 1 curcuit

Here is my problem. I replaced my old 200 amp breaker box with a new 200 amp one. I thought I was very careful in removing the old breakers by doing them one at a time by unhooking one at a time and pulling out the wire and reattaching the wire and letting the breaker hang on the wire. I did this for each and every one of them. I took out the old box and replaced it with the new one. I reversed the process by unhooking the old breaker one at a time and replacing it with a new one. When I was finished I turned them on one at a time and checked to make sure there was electric to the appropriate locations. Then I discovered that when I flipped one of them on then another would trip. I discovered that by leaving one of them off and turning on the other that the wire was hot all the way back to the other breaker in the box that I had turned on that tripped the breaker in the first place. I can leave one of the breakers off and everything seems to be working in the circuit. When I finished installing all the new breakers in the box I noticed that there was a piggy back wire left over that was about 1 foot long. There wire connected to the problem breaker appears to have been added by someone because it is defiantly not an original wire. I have lived here for several years and there has not been a problem with breakers tripping. I think someone had it rigged to work. Any suggestions please.