The Ukip councillor for Ramsey in Cambridgeshire, Lisa Duffy, has said she won't stand for the party leadership.
She was runner-up in the earlier contest which was won by Diane James who resigned just 18 days after being elected.
Following the resignation Ms Duffy, who finished second in last month's leadership election after gaining 4,591 votes, criticised Ms James for not showing sufficient leadership.
Lisa Duffy made the announcement that show would not run on BBC show Question Time last night.
It comes after Ukip leadership frontrunner Steven Woolfe resigned from the party just weeks after collapsing in the EU parliament following an altercation with a fellow MEP.
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