PROMOTED to the Premier League in 2011, they defied the odds to achieve a mid-table finish last term and lost their manager in the summer.
Norwich have followed a very similar path to Swansea City in recent times.
But while the two clubs' fortunes have closely matched, points have not been shared so evenly when they have met in recent seasons.
Norwich have become something of a bogey side for Swansea and were one of only three teams to do the double over them during the 2011-12 campaign.
Swansea did win a promotion tussle between the sides at the Liberty the season before that.
But only after Norwich had secured a fortunate victory in the reverse fixture when David Cotterill missed a late penalty with the score at 0-0.
Paul Lambert left for Aston Villa before the start of the season and Chris Hughton moved from Birmingham to replace him.
And there was more disruption when captain Grant Holt handed in a transfer request before eventually signing a new deal.
After a shaky start under Hughton, in which Norwich began with a 5-0 opening day defeat at Fulham and collected only three points from their first seven matches, the Canaries have begun to find their feet.
They head to South Wales just four points behind Swansea and will set a new record for their longest unbeaten run in the Premier League if they avoid defeat.
Norwich have not lost in their last eight top-flight matches, winning four and drawing four.
Hughton has made them harder to beat, a fact illustrated last Sunday when victory over Sunderland matched a sequence without loss stretching back 19 seasons.
They have been stronger at home, with victories over Arsenal and Manchester United, but they also had some joy at Goodison Park with a 1-1 draw against Everton.
"He has brought stability. He has made us harder to beat and you can see that from the goals conceded," said Bradley Johnson when asked about his manager.
"He is very keen on keeping clean sheets and now we don't look like we are going to concede goals in games. The manager has come in and seen last year perhaps that we were conceding a lot of goals.
"I think last year we had a motto of 'you score, we score' which probably wasn't good, even though we did well last year, but the manager has come in and brought some new players and they have done brilliantly for us.
"I think the fact that we are keeping clean sheets is good and now we just have to score a few more."