Double negation and litotes
Solution 1:
There's nothing wrong with your formation. You took the noun phrase "Something no-one has done before" and used it as a complement ("It is not [noun phrase]").
Incidentally, a double-negation is not an affirmation; it is a litotes. "It was not unlikely" does not mean "It was certain"; it might be neither likely nor certain. Only the negation of the first is clear.
Solution 2:
There's nothing per se "wrong" syntactically with double or multiple negation. In principle, the following sentence is perfectly grammatical:
He mustn't not never have done it to nobody.
and you can imagine that speakers might interpret this sentence by mathematically "unpicking" each negative just as you would unpick multiple negative signs when combined in a mathematical equation.
The problem is that this isn't actually how humans interpret negatives in natural language.
In reality:
- (a) although it has a "logical" interpretation, humans will typically find a sentence such as the above, with multiple negative elements, very difficult to interpret.
- (b) there is a phenomenon where, at least in informal English, the interpretation of multiple negatives can depend on the intonation, which is sometimes difficult to represent in writing and can also depend on register.
Point (a) is, I think, illustrated by my sentence above. You can probably understand each individual negative, or even individual pairs of negatives, perfectly well. But taken together, you've probably no idea what the sentence actually means. I know I haven't.
As an example of point (b):
"I haven't DONE nothing!" will generally be interpreted as an emphatic version of "I haven't done anything!"
"I haven't done NOTHING!" will generally be interpreted as an emphatic version of "I haven't done literally nothing, but rather something", "It isn't true that I have done absolutely nothing".
So pragmatically, for these reasons it's usually sensible to avoid multiple negatives in writing and rare to combine more than two in speech, bearing in mind that if you do combine them you may need to be careful with intonation, something that may not come easily to a non-native speaker. It's not that they're ungrammatical in principle. It's more that in practice they're difficult for speakers to deal with.
P.S. That said, I should have mentioned that multiple negatives are less problematic when each negative is in its own clause. So "I haven't done nothing" is maybe a bit harder to interpret than "It's not true that I haven't done anything". So if you must use a multiple negative, try and get each negative in its own clause.
Solution 3:
There are two kinds of double negation. One negates and the other affirms.
An example of the kind that negates is I ain’t done nothing. This means that the speaker has not performed any of the acts alleged. It most definitely does not mean that they have been committed. The construction is no longer allowed in Standard English, but is found in other dialects.
Your examples are of the second kind. It's not something no-one has done before means that whatever is under discussion has been done before. No-one hasn't done before is not a satisfactory alternative, not least because it risks being taken as the other kind of double negation.
There may sometimes be good reasons for using this second kind of double negation, depending on the context and the intention of the speaker. If there are no good reasons, then it is best avoided, because it forces the reader or listener to spend time untangling what you have said, instead of paying attention to what it is you are actually saying. If you really wanted to say something other than Someone has done this before, you could say It’s not as if no one has ever done this before.
Litotes uses two negatives to achieve an understatement as a way of saying the opposite of what the words themselves seem to mean. Not bad, for example, will often mean not just a little better than nothing, but ‘very good’.