No side has achieved that ignominious feat since the Vale of Leven in 1892.
Brechin lost their 36th and final game of the second-tier Championship season 5-1 at home to Queen of the South.
The town is located in the northeast of Scotland between Dundee and Aberdeen and its football team does not have any full-time professionals.
The team picked up just four points from four draws, finishing 26 points behind second-to-last team Dumbarton.
Championship winners St Mirren were 70 points ahead.
The day before the game, team officials had tweeted: “It’s the final game of what has been a very difficult season tomorrow.
“City will finish the season at the home against Queen of the South FC and will be hoping to finally get that elusive first league win!”
But it was not to be.