I agree someone knowledgeable should write down the steps of the procedure as well as inputs, outputs, criteria for acceptance, and any caveats. Maybe someone else formats and edits for readability.
Many times, the real value of a procedure is to train a new person, or guide a person who does not perform the procedure very often (perhaps a fill-in substitute in the case of vacation or other absence). If that is how the procedure will be used, a best practice would be to select such a person, knowledgeable but otherwise uninvolved in writing the procedure, who then attempts to follow the about-to-be-released procedure in a simulated or real life scenario.