The new man at the helm has never been an MP at Westminster, so he arrives with none of the baggage that goes with a past life on the green benches and in the Commons corridors.
Donald Dewar may have been dubbed the Father of the Nation for bringing about the Scottish Parliament.
And it was Henry McLeish who steered the devolution legislation through the Commons.
But both Mr McConnell’s predecessors came to the new parliament after years of operating on the Westminster scene. They were used to its formality, its traditions, its clubbish ways, the yah-boo politics and the behind-the-scenes deals.
Jack McConnell is the first First Minister to have been shaped by the Scottish Parliament itself.
No-one doubts the sharpness of his political skills, honed during years at the centre of the Labour Party in Scotland.
But so far as the parliament is concerned, he will be untainted by Westminster ways.
And his accession to the post could herald changes in the way parliament runs.
Presiding Officer Sir David Steel has revealed his own dislike for First Minister’s Questions, describing it as "something of a caricature of Prime Minister’s Question Time," which he regards as "not a healthy aspect of parliamentary democracy at all".
So could we see the end of the regular Thursday afternoon session of gladiatorial combat?
The Scottish Parliament, of course, started without any time set aside for the First Minister to be grilled by MSPs. And Sir David seems to think it was better when all oral questions were addressed to the Executive in general, with some of them being answered by the First Minister.
The system was changed because people felt they were being denied the chance to put the top man on the spot and Donald Dewar agreed.
The verbal sparring matches between Mr Dewar and the then SNP leader Alex Salmond were often a highlight of the week’s business. The same could not often be said for the confrontations between their successors, Henry McLeish and John Swinney.
But Mr McConnell is a good performer and quick on his feet. He might see how he fares before making changes.
Sir David has said he thinks the current four-minute limit on most speeches in the parliament is too short and many politicians feel the same. But hopefully the limit wouldn’t be lifted altogether so it ends up like the Commons, where backbenchers can drone on for hours about little.
Meanwhile, the new First Minister is already instituting other changes in the style of government.
He has let it be known he does not plan to have a special adviser as chief spin doctor in the way Donald Dewar had David Whitton and Henry McLeish had Peter MacMahon. Instead, it is said, he will use civil service press officers who will stay clear of comment on policy.
And Mr McConnell is trying to get away from the traditional Cabinet reshuffle where a procession of ministers can be seen coming and going, feeding speculation about sackings and appointments.
One aide says: "Jack doesn’t want to do the usual thing of calling people in and saying ‘You’re in’ and ‘You’re out’. He wants to talk to people about it all."
He has been holding meetings with ministers and others and is understood to be discussing changes to portfolios as well as personnel.
And when the line-up is revealed next week, it will be born out of that process.
The changes in style and shifts of emphasis may not make a big impact on the day to day lives of the people . But it appears the Scottish Parliament is gradually growing up and successfully distancing itself from Westminster.