Mr Parry, who has recently resigned from the group, insists on still being called independent but the ruling group is insisting that he be called something else to avoid confusion.
However, Mr Parry said: 'I'm a real independent. I don't follow any party line and I vote on each issue as it comes up by what I feel is the best for Pembrokeshire. How can you be independent and in a party?'
The council solicitor has suggested that he be called Independent (Unaffiliated), but Mr Parry says this is nonsense because independent means unaffiliated.