Lincoln lost their Football league status as they lost 3-0 at home to Aldershot.
A near 8,000 crowd saw the Imps hand in their place with little fight, while Barnet netted a penalty to retain their spot in the 92 by a solitary point.
Falling into League Two are Dagenham after they lost at Peterboro. They join Swindon, Plymouth, and Bristol Rovers in the bottom four.