Zimbabwe's central bank says banknotes from its old currency, which collapsed and was discarded years ago because of runaway inflation, can be exchanged for American dollars.
But 100 trillion Zimbabwean dollars will fetch only 40 US cents.
That's a fraction of what collectors have been paying for the notes with numerous zeros for years.
Zimbabwe in 2009 abandoned its currency for a system dominated by the US dollar and the South African rand after inflation hit 230 million per cent.
Back then, even street hawkers refused to accept a $100 trillion dollar note that was issued.
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Starting on Monday, stacks of Zimbabwean bills that might still be kept by Zimbabweans can be exchanged for US dollars.
The offer is part of what the central bank says is an overdue plan to phase out the currency entirely.
Some people in Harare, Zimbabwe's capital, said they disposed of their Zimbabwean dollars long ago.
"I used it as garden manure," said Isaac Mutezowepasi, a street vendor.
"Why would I have kept that dirt?"
Others said they still have heaps of old dollar notes at home, but won't respond to the government offer.
"I am keeping them for my grandchildren to see. Plus I know I will get more for them in future because these Zimdollars are going to be in demand," said Tendai Nyaundi, a graphic designer.
On eBay on Friday, five banknotes of 100 trillion Zimbabwean dollars were being sold for $US159 ($A205).
Another eBay post put five banknotes of $100 trillion at $US173.99.
There have been calls to re-introduce the Zimbabwean dollar by some members of President Robert Mugabe's ruling ZANU-PF party.
They argued that the use of foreign currencies is responsible for the country's current liquidity problems.
Finance Minister Patrick Chinamasa has repeatedly said the US dollar "is here to stay."
