Translation:It is not Kati who has a necklace, but me.
Another note for people who are learning English: formally, this sentence should read It is not Kati who has a necklace, but I. This is because English doesn't use the accusative case (me) with the verb to be.
However, using but me is not necessarily bad or wrong here - in fact, it's the way many native speakers would say it.
But that's because English speakers (myself included) are usually terrible at using the accusative. It only matters if you are trying to get 100% formal correctness.
True that often native speakers mess up using me instead of I, but the particular formal structure of this sentence is such non-colloquial english that the mistake is especially blatant here and should be fixed.