Current chairman Pierre Horsfall and incoming chairman Gerald Voisin say that the debate should be open, as it was when Mr Horsfall was appointed by the States in 2002.
Last Wednesday the States discussed a proposal to replace Mr Horsfall with Mr Voisin in secret for an hour and a half.
The next day Members said that the debate had included ‘vitriolic character assassination’ of Mr Horsfall, but the Standing Orders of the States Chamber would require a States decision to release the tapes or the transcript.
Mr Voisin, who takes over the WEB chairmanship on 20 August, said that he was not concerned about the transcript either way.
‘As far as I am concerned the matter is entirely for Pierre Horsfall to pursue,’ he said.