The survey of more than 1,000 people was taken in the days around the publication of the Scottish Government's White Paper on independence.
The results show 26% back a Yes vote, up one point on polls from September and October.
Backing for a No vote, at 42%, is one point down on October and two points down on September, the poll by TNS BMRB suggests.
Around one-third remain undecided.
Among those who say they are certain to vote, the results change to show 31% support for independence and 46% against.
Tom Costley, head of TNS Scotland, said: "It's almost as if opinion in Scotland was marking time before the publication of the White Paper.
"Once we get into 2014, we can expect the debate to gather pace ahead of the September referendum, and we may begin to see some shifts in opinion, especially with so many people clearly waiting to be convinced one way or another. The examination of the White Paper will be an important part of that debate."
The results come days after a different poll was taken on attitudes to independence after the release of the White Paper.
The separate survey, conducted by Progressive Scottish Opinion, put support for a Yes vote at 27% and support for a No vote at 56%.
A Better Together spokesman said: "The fact that support for Scotland going it alone remains below historic levels shows that people are increasingly rejecting Alex Salmond's politics of division and grievance.
"Although this poll is encouraging, there is no room for complacency. The Nationalists only need to win once and by one vote to break up the UK forever.
"We will be campaigning every day to make our strong positive case to people who have yet to make up their mind that we are stronger and better together as part of the UK."
Blair Jenkins, chief executive of Yes Scotland, said: "Yet another poll shows a shift away from No to a Yes vote, leaving a third of voters in Scotland still undecided. This means a swing of less than 8% would put the Yes vote in front.
"The No campaign has lost almost one-fifth of its supporters over the last year, which is not surprising given the 'can't do' negativity of a campaign that describes itself as 'project fear'.
"It is now clear what a Yes vote will mean for Scotland, with important gains and guarantees for people across the country.
"The big question marks are over the costs of a No and that is why their support is in freefall."