Emma Macdonald has been appointed as the new leader of the SIC.
Members voted in a secret ballot as the second item of business at their first official meeting.
The nominees were Mrs Macdonald and Stephen Leask. Mrs Macdonald won 11-9 votes.
Mrs Macdonald, who was previously depute leader, said she was “hard working, motivated and positive”.
“More importantly, I’m extremely passionate about local government and local decision making.”
Mr Leask said he would seek to foster an “open door policy”.
He said he would welcome the valuable experience of existing members and the innovative contributions of new councillors.
After being voted in, Mrs Macdonald nominated Gary Robinson to be depute leader.
The role requires its holder to provide “political leadership and direction”.
It is the most senior position within the council commanding a salary of £32,622.
Prior to the meeting, rumours about who might be putting themselves forward included Mr Leask, Mrs Macdonald and Ryan Thomson, although Mr Thomson later confirmed he had withdrawn.
The role was previously held by Steven Coutts, who stood down from the council at the end of the last term.