Backing for a Yes vote in September's referendum has fallen to 35 per cent, while 54 per cent said they would vote No, a YouGov poll said.
A further 10 per cent said they were undecided, while two per cent said they would not vote.
Without undecided voters or those who would not vote, the results were 39 per cent for Yes, and 61 per cent for No.
The results represent a slight decrease in support for independence, and a slight increase in backing for a No vote compared with the last YouGov poll for the newspaper in March.
Better Together campaign director Blair McDougall said: "This poll is a major setback to Alex Salmond's negative and divisive campaign. The more people think about the consequences of breaking up the UK for jobs, pensions and public services, the more they are saying No Thanks.
"There will be no let-up from our campaign over the summer. We have a positive vision for Scotland that is winning over swing voters."
A spokesman for the Yes Scotland campaign said: "The polls will fluctuate from time to time, but we believe our positive message, that only with independence can the wealth of Scotland work for all the people, will be successful in September."