In the Old Testament there's a fantastic word Tsedeq which usually goes alongside Mishpat. They're great words - the first means righteousness whilst the second means justice. And justice as we all know is a brilliant thing. So perhaps is righteousness!
Righteousness has nothing - absolutely nothing - to do with self-righteousness.
Just as every sin has a relational aspect (either towards God or humanity or creation) so righteousness speaks of the opposite of sin. It is relational rightness with God, with other humans and with creation. It is a constant lifestyle of doing that which is 'right' for any other person in any circumstance.
Righteousness is the opposite of sin, it is justice personified. It is Good News!