It comes after a Swedish-born teacher was unsuccessful in her bid to take the post following an interview for the job yesterday.
Annika Jansson, who had been deputy head of a primary in Nairn but has been acting head at the Gaelic primary on the southern periphery of Inverness since the summer of 2010, is understood to have applied for the post.
Although not a Gaelic speaker, Ms Jansson had a good reputation as a manager, but parents were reported to be unhappy with the prospect of a non-Gaelic-speaking head.
She was one of only two applicants, neither fluent Gaels. The other subsequently withdrew leaving Ms Jansson.
Three councillors and three members of the parent council were on the interview panel
Afterwards the council issued a statement: "The Highland Council were today [Monday] unsuccessful in appointing a permanent head teacher to the post at Bun-sgoil Ghàidhlig Inbhir Nis [Inverness Gaelic Medium Primary School]." Parents of the 169 primary and 94 nursery pupils believe that to protect the ethos of the school, whoever gets the £48,000-a-year job should be fluent and literate in Gaelic, although not all are themselves.
However this time, following discussions with the statutory body Bòrd na Gàidhlig and the Scottish Government, the council dropped the requirement for fluency, opening it up to teachers with an interest in learning the language.
The council prepared to provide extra support in the event of a non-Gael being appointed, including a review of how management, the staff and others could ensure that as much Gaelic as possible was spoken beyond the classroom – for example, at assemblies and school events.
Now the search continues in the long saga of appointing a suitable candidate.
The first and only head teacher for Inverness Gaelic Medium Primary School was appointed prior to the school opening in August 2007 and remained in post until April 2009.
Since then there have been three acting head teachers in the school.