Ministers bowed to pressure from the largest teaching union and agreed to make the change to the controversial performance-related pay scheme.
The National Union of Teachers argued that the Order which came into force last month infringed teachers' employment rights.
The Government has conceded that there should be a third check on headteachers' judgments. If a teacher fails to cross the threshold after being judged by their head and checked by an external assessor, they may already apply to have a second assessor to review the case.
Under the amended order they will now be able to refer their case to their employer, either the local authority or te governing body in the case of voluntary-aided or foundation schools. If the employer upholds the original decision, then the teacher can take the employer to an industrial tribunal.
The Government has also agreed to the union's demand to give unattached teachers the same rights as staff employed in schools to apply to cross the threshold.
The Department for Education and Employment will consult on the amended Order until January 31.
Doug McAvoy, NUT general secretary, said: "At last the Government is seeing sense. The original procedures were shot through with legal holes which undermined teachers' rights."
But John Dunford, general secretary of the Secondary Heads Association, said it would make the threshold process even more complicated.