The latest poll on the flag referendum shows almost two thirds of those surveyed are in favour of keeping the current flag.
According to the research company, UMR, there is a group in favour of changing the flag but who do not like the alternative design, and that group could make a difference to the outcome.
The survey undertaken in the last week of February showed 59 percent of people wanted to keep the current flag, 32 percent wanted to change it and 9 percent were unsure.
National Party voters were evenly split between keeping the current flag and retaining the old one, but opposition voters overwhelmingly supported keeping the current flag.
Of those spoken to, 66 percent said they were almost certain they would be voting in the referendum. More men supported change compared to women.
Previous UMR surveys showed almost 20 percent of those voting to maintain the status quo would in principle like to see a change but did not like the alternative design.
UMR's executive director, Stephen Mills, said he believed that those voting for the current flag because of its tradition and history were unlikely to change their stance, and neither would those who supported the Kyle Lockwood design for the values it reflected.
But he said 20 percent, who in principle agreed with a flag change but did not like the design, were more likely to switch their vote.
"The retention campaign just has to hold them and the change campaign has to move them. So they [campaign for change] have got the harder task, but they're the ones that could still, I think, alter the result."
However, Mr Mills said that all the available polls that had been done on the flag referendum pointed to no change.
The UMR survey spoke to 750 people by telephone between the 25th and 29th February.
The poll had a margin of error of + / - 3.6 percent.