Research by Survation suggests 52% of Scots back the country leaving the rest of the UK – a drop of two percentage points from November.
The figures are based on those expressing a voting intention once respondents who are undecided or refuse to answer are removed.
When undecided voters are included – at 16% – then 43% are Yes and 41% are No.
The SNP stressed it is the 16th consecutive poll showing a majority in favour of independence.
Looking at voting intention in the next Holyrood election, the pollsters said Nicola Sturgeon’s party retains a “commanding lead” over the other parties in the constituency section of the vote, although this dropped by 1% from last month to 53%.
The Tories and Labour are neck and neck on 20% – with Labour up two points on November and the Conservatives up by one point.
The Liberal Democrats are on 6%, with 1% of respondents saying they will vote for another party.
In the regional section of the ballot, support for the SNP is 41%, down one point from November.
Backing for Labour is up one point to 20%, with support for the Tories increasing by the same amount to 18%.
Meanwhile, 10% said they will vote for the Greens on the regional ballot, 7% back the Lib Dems, 1% are in favour of both the Brexit Party and UKIP and less than 1% support other parties.
Survation published the research after questioning 1,018 people aged 16 and over between December 4 and 9.
SNP depute leader Keith Brown said: “Once again, a poll shows that independence is becoming the settled will of the people of Scotland, now with 16 polls in a row showing majority support.
“An independence referendum will be the choice of the people of Scotland and they will make that decision at the ballot box in May, not Boris Johnson.”
Mr Brown added: “The SNP will take nothing for granted and continue to work hard to gain the trust of voters ahead of the Scottish election in 2021.
“However, these polls continue to show that the people of Scotland believe our best interests are served as an independent country.”