The Pauli Exclusion Principle (PEP) is one of the basic principles of modern physics and, even if there are no compelling reasons to doubt its validity, it is still debated today because an intuitive, elementary explanation is still missing, and because of its unique stand among the basic symmetries of physics. The present paper reports a new limit on the probability that PEP is violated by electrons, in a search for a shifted K$_alpha$ line in copper: the presence of this line in the soft X-ray copper fluorescence would signal a transition to a ground state already occupied by 2 electrons. The obtained value, ${1/2} beta^{2} leq 4.5times 10^{-28}$, improves the existing limit by almost two orders of magnitude.
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