An Ipsos Mori poll for the Times and Sun newspapers showed the number of people who thought Scotland should be independent had dipped 4% since January.
A total of 1,000 people were asked: "Do you agree Scotland should be an independent country?" - the preferred wording of the proposed referendum on Scotland's constitutional future.
Of those who said they were certain to vote, more than half - 55% said they did not agree - up 5% since January, while 35% said yes.
Amongst all voters, including those who were not sure if they would vote or not, 32% agreed with Scottish independence, and 55% disagreed.
Scottish Labour leader Johann Lamont said: "This shows that the more people hear the arguments, the more they see through the absurdities of Alex Salmond's case for separation and the more they recognise the benefits of Scotland's partnership in the UK.
"This debate can reinforce Scotland's place in the UK and let us get away from this constitutional bickering and concentrate on the the real issue - how we improve life for each and every Scot."