THERE IS LITTLE doubt that the refusal of a North Carolina jury to convict four Klansmen and two Nazis of murdering five Communists will be widely publicized as another example of how injustice still reigns in the good, old, bigoted USA. The facts seem so simple. The Communists were shot to death; the Klansmen and Nazis fired at them; and almost everyone saw the terrible incident on television news. How could a jury, except one infuriated with the political views of the victims and infatuated with those of the defendants, return a verdict of not guilty?

But the facts on which murder convictions should rest do not appear to have been so straightforward when they were presented in that Greensboro courtroom. The trial lasted 23 weeks, and the jury deliberated for seven days. Some of those at the scene of the massacre -- friends and survivors of the victims -- refused to testify.The Klansmen and Nazis pleaded self-defense, and the prosecution had difficulty establishing which group attacked first. It was obvious that both groups were spoiling for a fight that day.

Did the jury render a proper verdict based on the evidence it heard? Was the prosecution as vigorous and as precise as it could possibly be? Was self-defense a smokescreen or a legitimate defense? We don't purport to know, and we doubt that anyone other than those who sat through all of the trial is in position to provide an authoritative opinion.

But fortunately, a mechanism exists that can help provide answers to these important questions. Under the civil rights laws, the Department of Justice can investigate the case, examine the evidence and initiate a federal prosecution if there was a conspiracy to deprive the dead people of their constitutional rights. It should act promptly. If a gross injustice has been done by that jury, a federal prosecution can remove a part of the stain. If an injustice has not been done, the federal govenment can help establish that by providing an evenhanded, non-political review that will be acceptable to all but those few who, from the beginning, may have been intent on creating martyrs and heroes out of this tragedy.