The Herald, owned by Newsquest, reported an average daily readership of 130,000 in the period July 2009 to June 2010, a fall of 39% on the previous year.
Its Sunday stablemate, the Sunday Herald, was also hit by a steep fall, shedding 28% of its readership, to 121,000.
The Scotsman, owned by Johnston Press, fell 29% to an average readership of 131,000, while the Glasgow Evening Times dropped 22% on the year to 139,000.
The Herald, like its rivals, has been hit by the general trend of consumers turning away from the printed medium. A price promotion by its rival, the Scottish Daily Mail, which reduced its cover price in the west of Scotland from 45p to 20p, is also likely to have impacted sales of the broadsheet.
However, the steep falls in readership have not been mirrored in the latest round of ABCs figures for the two titles.
According to ABCs, the circulation of the Herald dropped 6.8% year on year in July to 52,182, while the Sunday Herald fell just 1.1% to 40,069.
The NRS surveys 36,000 people to estimate newspaper readership, unlike the ABC, which audits the number of copies of papers distributed.
The Herald’s new editor, Jonathan Russell, a former assistant editor of the Daily Record, has looked to woo readers with design changes.
Jenny McManus, press account manager at media agency Feather Brooksbank, said the appointment of a new editor had meant "much bolder front pages, bigger pictures and, in general, making better use of the broadsheet".
She added: "There are plans to increase print runs going forward, to minimise out-of-stock situations, in the hope that we should see small increases on ABC and NRS at the next survey."
Across the London-based titles, the London Evening Standard registered a readership of 1.41 million, up 132% on the year.
However, this is not a like-for-like comparison, as it is comparing a 50p paid-for title with a free title, which ballooned its distribution to 600,000 in September last year.
Evening Standard editor Geordie Greig said: "It is great news for the Evening Standard and for all Londoners, that more people are reading the paper than at any time in its history."
The data reveals that the Daily Star, the Daily Star Sunday and the Daily Mail were the only UK-wide papers to increase their readership in the period.
The Daily Mail rose 1% to 4,896,000, while the Daily Star added 8% to 1,586,000.
The biggest fallers were The Independent, which fell 11% on the year to 607,000 readers, and the Daily Express, down 10% to 1,624,000.
Across the Sunday market, the biggest faller was The Observer, down 17% to 1.14 million.