The fingerprinting system is supposed to cut costs and stop kids having to carry library cards around.
Each child has their thumb scanned, which is stored in a computer and used to prove their identity every time they borrow a book.
'Should be banned'
But Human Rights group, Privacy International, says this is illegal and wrong.
It thinks fingerprinting should be banned in all schools.
Around 200,000 school children have been fingerprinted for this new system in the UK.
But it's thought there might be legal challenges to stop the fingerprinting happening.
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