Procedural justice is a legal term, concerning the fairness and the transparency of the processes by which decisions are made.  In  USA,  The concept of Procedural justice is reflected in so called Due process that  requires the state must respect all of the legal rights that are owed to a person,  follow the full and exact course of the law.  Its purpose is to protect individual persons who lack of power

Using everyday language , it means to stick strictly with the rule regardless of its results even it may be injustice by common sense.

While procedural justice obviously could be challenged theoretically, particularly literally,  and also caused many mistake cases in practice,  it is still fundamentally better than an arbitrary justice that based on will of superiors and requirement of politics