Local government minister George Kynoch said last month the aim of the task force was to examine the role and scope of the ombudsman, the National Code of Local Government Conduct, the Register of Pecuniary Interests, the arrangements for appointing and dismissing senior officers and the system of monitoring officers.
The task force has three representatives from the Scottish Office environment department's local government division: Mr Graham, George Thomson and Debbie Neale.
Six other members of the task force, nominated by the Convention of Scottish Local Authorities, are retiring local government officials.
COSLA president Rosemary McKenna said she wanted the task force to produce concrete proposals to ensure allegations against councils could not remain unsolved for lengthy periods.
'It is vital accusations about misconduct or irregularities in local government are dealt with fully and fairly, at an early stage. They must not be allowed to go unchallenged and be blown out of proportion.'