Come on man wiki sucks, haven't you heard?
True, you can't always depend 100% on Wikipedia, because it is edited by "ordinary people" like us, so before quoting Wikipedia, it is best to find other sources as well.
In this case, I checked a number of other sources, including
dictionary.com, which is based on the dependable Random House Dictionary, and says:
paper currency made legal tender by a fiat of the government, but not based on or convertible into coin.
The
Oxford Dictionaries, another reputable source, says:
Inconvertible paper money made legal tender by a government decree.
Also most of the "business" or "investment" online dictionaries agree with these.
On the other hand, another dependable dictionary,
Merriam-Webster says:
money (as paper currency) not convertible into coin or specie of equivalent value
...so that would fit your definition.
In summary, with one exception I found, most English dictionaries define fiat currency as decreed by government.