EMB170 First Officer arriving DFW on the BYP5 experiences the FMC reinitializing the arrival from the beginning after a runway change. Error goes unnoticed until 90 degrees of heading change have occurred. Situation is reported to have occurred during arrival to LGA also.

Narrative

We were on the Bonham arrival into DFW. As the flying pilot I had briefed ILS 17C; and inputted it into the FMS. We were descending through seven thousand when we were handed off to approach; who gave us ILS 17L. I changed the runway in the FMS but didn't follow verification procedures. I turned away to brief the approach without confirming my change with the Captain; or noticing that the FMS has added all the fixes in the arrival instead of adding just the fixes that we hadn't crossed. Autopilot started making a right turn back to the beginning of the arrival and was about 90 degrees off course when I finished briefing the approach and I looked back up. The Captain was also looking for his chart and did not notice the change in heading. I turned back to our course heading. ATC then gave us a heading for vectors to the approach.Always follow verification procedures no matter how small the change in the flight plan. If time is a factor; have the pilot not flying brief the approach. Fix the software in the FMS in DFW and LGA where it adds all fixes in the arrival with a change in runway instead of adding the fixes that haven't been crossed.