The Committee of Scottish Clearing Bankers recorded 2465 start-ups in Scotland in the three months to December, down 20% on the preceding three months, when 3097 businesses got going.
The number of start-ups was 9%, 251, lower than the 2716 recorded in the same quarter of 2012.
The figures are based on the number of new business accounts opened with Royal Bank of Scotland, Lloyds Banking Group's Bank of Scotland and Lloyds TSB operations, and Clydesdale Bank.
This has long been seen as a way of gauging the success of efforts to boost the business birth rate in Scotland.
The total number of start-ups recorded by CSCB members in the full year fell by 15% in 2013, to 11,679, from 13,856 in 2012.
The slump seems to have been driven by a big fall in the number of people moving into self-employment.
The number of sole traders fell by 304, or 30% in the last quarter, to 690 from 994. The number of sole-traders also fell by 30%, or 1681, over the full year, to 3816 from 5497.
The fall may have been a product of the broader economic recovery that took hold last year.
Many people who were laid off during the downturn that started in 2007 may have set up their own businesses as jobs in industries such as construction were in short supply. The number of construction start-ups fell by 25% annually in 2013, to 1117, compared with 1490 in 2012.
The 20% fall in the number of hotel and restaurant start-ups in 2013, to 1148 from 1430 in 2012, more likely reflects continued tough conditions in some sectors.
Some experts said the underlying picture was brighter than the headline-clearing bank numbers indicated.
Hugh Lightbody, chief officer at the national unit of the Business Gateway advice service, said the number of new companies set up with its help to the end of December was 7% higher than the same period in the previous year.
He noted a recent report from the Federation of Small Businesses in Scotland showed that the number of new company registrations at Companies House was up 18% in 2013.
Mr Lightbody noted: "The Committee of Scottish Bankers' data is made up only by four high street banks."
Colin Borland, head of external affairs in Scotland for the Federation of Small Businesses, said research findings indicated confidence had been increasing among its members.
A spokesman for the Scottish Government said: "Official business start-up data from the Office for National Statistics shows that the number of new VAT/PAYE registrations have increased in Scotland for the third consecutive year."
The clearing bankers found 7003 companies started up in 2013, down 4% on the 7277 recorded in 2012. The number of partnerships starting up fell by 20%, to 860 in 2013, from 1082 in 2012.