Other forms: extrajudicially
Something that's extrajudicial isn't backed or upheld by the law. Taking revenge on someone instead of taking them to court is an extrajudicial punishment.
If a prisoner is executed without an official trial in a court, it's extrajudicial, and if police officers shoot and kill a suspect instead of arresting him, that would also be extrajudicial. Both examples happen outside of the legal process, and without the checks and balances that the law provides. Extrajudicial comes from the Latin root words extra, "outside of," and iudicalis, "belonging to a court of justice."