Councillor Tommy MacPherson (Conservative, South Kintyre), who was only elected as a ward councillor in May, said he had 'serious misgivings' as to how The Argyll, Lomond and Islands Group (TALIG) operates.
He says he intends to remain a councillor for the ward, but will also relinquish his position as deputy policy leads for roads and infrastructure.
However, councillor MacPherson gave no further indication of the nature of the concerns that led to his decision.
The TALIG group consists of a coalition of Conservative, Liberal Democrat and some independent councillors.
Announcing his decision on social media, Councillor MacPherson said: 'I have today given my notice as member of the Argyll and Bute Council administration.
'I have serious misgivings as to the modus operandi of TALIG, therefore I have taken the decision to resign as deputy policy lead for roads and infrastructure and from the TALIG administration group.
'I remain stedfast to my South Kintyre constituents whom I will continue to serve to the best of my ability.'
The independent Lomond North councillor Mark Irvine said: 'I applaud your ethics and your commitment to your electorate. You have taken a stance and your constituents are lucky to have someone with the backbone and fortitude to do what you think is right. Fair play to you.'
The independent Kintyre and the Islands councillor Alastair Redman said: 'I'm sorry to hear this Tommy. I hope to continue working with you on local issues for both of our wards.'
Councillor MacPherson replied: 'My greatest reward these past seven months has been the case work assisting individuals and families, South Kintyre constituents, on a wide spectrum of local issues. With your assistance and support, I plan to continue.'
Councillor Redman regained his old job as policy lead for economic growth in November, giving the TALIG coalition a majority of two. Councillor MacPherson's resignation now reduces that knife-edge majority to one.
The leader of the council and TALIG, Robin Currie, pledged that the administration will continue ‘business as usual’, despite Councillor MacPherson's resignation from the group.
Councillor Currie (Liberal Democrat, Kintyre and the Islands) insists that the administrative group will continue to focus on delivering its priorities, which were recently agreed unanimously by the full council.
He said: 'I received notification of Councillor Macpherson’s decision earlier today (Wednesday). In the meantime, as an administration we will continue our business of leading the council as a group who work well together and who have a shared vision for Argyll and Bute.
'That collective vision is set out in the priorities that this administration developed and which were unanimously agreed by council last month.
'Delivering on that vision has always been, and will remain, our top priority, and getting on with the job at hand is our main focus.'
In his resignation letter, sent to The Oban Times on Thursday morning, Councillor MacPherson said: 'I hold centre right conservative cultural economic attitudes and values. I view myself as a Right Libertarian. My priorities are focused to that of the individual not the public authority.
'I was elected to represent South Kintyre constituents, who have remained my primary focus throughout. I joined the TALIG Group forming an Administration in the understanding I would serve and represent, through local government, the best interests of the wider community of Argyll & Bute.
'In recent weeks I have raised searching questions within the Administration as to the functionality of TALIG. Quintessentially, what does TALIG stand for, the Conservative Group's position within the TALIG and TALIG's modus operandi with officers and opposition members?
'For what is being played out on a weekly basis I would be negligent in my elected duty to continue having my misgivings marginalised.
'I have therefore taken the decision to resign as Deputy Policy Lead for Roads & Infrastructure and from the TALIG Administration Group.
'I remain steadfast to my South Kintyre constituents whom I will continue to serve to the best of my ability.'
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