The St. Paul Police Department is investigating an officer who wrote a Facebook post encouraging people to run over protesters on Martin Luther King Jr. Day. Typically we wouldn’t prejudge the outcome of such an investigation. But in this very clear and public case, the ultimate step is clear: Sgt. Jeffrey M. Rothecker should be fired.

And once he is terminated, the dismissal should stick. Neither the police union nor an arbitrator should come to Rothecker’s defense.

“Run them over,” Rothecker wrote on Facebook, using the name “JM Roth.” “Keep traffic flowing and don’t slow down for any of these idiots who try and block the street.”

He was referring to Black Lives Matter marchers who have held a series of protests after officer-involved shootings, including the deaths of Jamar Clark in Minneapolis and Marcus Golden in St. Paul.

Rothecker, a 22-year St. Paul police veteran, was placed on paid administrative leave after an open-government activist alerted the department to the Facebook post. Not only did Rothecker encourage violence, he also gave advice on how drivers could likely avoid charges by pulling over and calling police.

Rothecker has apologized for the post, so there is no question that he wrote it. But his mea culpa rang hollow when it was revealed that he had made similar online remarks before. A spokesperson for the group Minnesota Neighborhoods Organizing for Change posted comments that “JM Roth” wrote a few months before in which he also told motorists to run over protesters.

Certainly, anyone is entitled to an opinion about Black Lives Matter. But officers are not just anyone. Police officers should be held to higher standards. They are paid to keep communities safe and catch criminals — not to encourage criminal acts.

In a similar case, the Cleveland Police Department placed an officer on leave while investigating online posts in which he allegedly insulted and blamed the mother of Tamir Rice, the 12-year-boy who was shot and killed by an officer. An officer, who was a school resource officer working with kids Tamir’s age, called the boy’s mother a derogatory name who shouldn’t have let her son out with the toy gun he was carrying when he was killed.

How can the public be expected to trust law enforcement when officers display such contempt for the citizens they should be serving? And why should the majority of dedicated public servants who protect our communities have to work with rogue officers who damage community relations and make doing difficult jobs even harder?

We trust that improved pre-screening of police candidates will help leaders eliminate those with the wrong temperaments before they receive a badge and a gun. But when that screening fails or veteran officers turn against the people they are supposed to protect, they should lose their jobs.