Hibernian chief executive Leeann Dempster has decided not to be part of the SPFL task force focusing on league reconstruction.
Dempster was one of 15 names on the initial list when the task force was announced last week to look into the future of Scottish football when all divisions return to action in the wake of the coronavirus pandemic.
She will instead focus on being part of a series of SPFL committees, announced on Monday, who will deal with the potential return of Premiership football later in the summer.
Those committees will concentrate on planning for that return, whether supporters will be allowed, and a number of medical, broadcasting and regulatory matters.
The reconstruction task force met for the first time on Monday afternoon, chaired by Hearts owner Ann Budge and Hamilton Academical chairman Les Gray.
That meeting involved 12 other members, four from the Championship, three each from Leagues One and Two and single representatives from the Highland and Lowland leagues.
They were due to talk about the possible future structure of the domestic game, which was brought to a halt last week when all divisions below the Premiership were finished on a points-per-game basis.
Livingston make proposal public
Later on Monday, Premiership club Livingston put their proposal for the future of Scotland's four divisions into the public domain, involving a 14-team top flight and promotion for the winners of the Highland and Lowland League every season.
Their statement read: "We believe that permanent league reconstruction is the most progressive way forward for Scottish football as a whole. The introduction of Highland League and Lowland League champions every year into the SPFL will bring the total number of clubs from 42 to 44 and this would have a minimal financial effect on current clubs.
"We feel it is fundamental to the sporting integrity of Scottish Football that no club suffers the financial effects which relegation would bring, as a result of the remaining league games not being fulfilled."
As things stand, should no further games be possible, Hearts would be relegated from the Premiership with Dundee United - already crowned champions of the cancelled Championship - taking their place.
Raith Rovers will be promoted from League One to replace relegated Partick Thistle, while Cove Rangers - champions of League Two - would take the place of relegated Stranraer in League One.
Highland League champions Brora Rangers and Lowland League winners Kelty Hearts are also waiting on what the future holds.