The Department of Education has found that no student benefited from an alleged attempt by an examiner who worked in a grind school to help students cheat in this year's Leaving Certificate chemistry paper.
A spokesman for the Department said they had examined all the chemistry papers and were satisfied that the marks for the students were "appropriate and correct".
He added: "The examiner in question did not help his students in any way.
"The students did not gain in any way. They did not get extra marks."
He said the investigation was continuing into other aspects of the matter.
A week ago the Department became aware of allegations that a Dublin chemistry teacher who also taught part-time in a grind school suggested a system to get his students higher marks.
It was claimed he told his grind school students to put the symbol of a bow tie on their papers and that he would look favourably on them if he came across them during his work as an examiner.
The Department said that every one of the chemistry papers had been examined and they had identified some papers with the symbol on them.
Of these, only 10 had been marked by the examiner in question.
When these papers were remarked it was found that the marking was "appropriate and correct, so he did not help anyone".