Mr Trimble resigned in July in protest against delays in the terrorist group the IRA getting rid of its weapons.
The IRA's political wing Sinn Fein has always demanded British soldiers should leave Northern Ireland.
But the IRA's decision to put some of its weapons beyond use last month breathed new life into the peace process.
After that Mr Trimble said he was willing to resume his post.
But in Friday's vote he couldn't rally enough support from his own side.
Britain will now have to decide whether to suspend the assembly or call new elections.