The Greek katakrisis (from kata- + krino, to judge down/against) means condemnation, a verdict of guilty. It appears twice in 2 Corinthians 3:9, where Paul contrasts the 'ministry of katakrisis' (the Mosaic covenant bringing condemnation, because it reveals sin but cannot remove it) with the 'ministry of righteousness' (the new covenant in the Spirit). The word is closely related to katakrima (G2631, condemnation as verdict).
Paul's use of katakrisis in 2 Corinthians 3:9 is profound: the Law, holy and good as it is, produces condemnation because it exposes sin without providing a remedy. The new covenant ministry is 'much more glorious' precisely because it brings righteousness instead of condemnation. This is the heart of Romans 8:1: 'There is therefore now no katakrima for those in Christ Jesus.' The ministry of condemnation has been superseded — not because sin is ignored, but because Christ bore it completely.