Mortgage rates have been falling as the Reserve Bank has made cuts to the official cash rate, which was reduced by 25 basis points to 3 per cent in July.
With the economic outlook darkening, some economists are picking the OCR to be cut further to 2.5 per cent - back where it was set during the global financial crisis.
Another OCR cut is expected next week.
High levels of competition among banks are also driving mortgage rates lower.
BNZ's new one-year rate has undercut a 4.49 per cent rate HSBC has been offering to its "premier" customers.
Massey University banking expert David Tripe said there was scope for mortgage rates to track even lower, possibly below 4 per cent.
"If we see sub 4 per cent rates it will be because the economy has got somewhat grimmer," he said.
Tripe described BNZ's 4.35 per cent rate as an "advertising measure" that would "get people in the door".
"A one-year fixed rate is not incredibly attractive because in one year's time rates will probably be going up," he said.
"What I suspect would be of much more interest to borrowers would be [lower] fixed rates for longer terms."
