MAJ. ARTHUR NICHOLSON, the American officer the Soviets murdered in East Germany on Sunday, was traveling in uniform, unarmed, in a marked military car, in daylight. He had been accredited by the Soviet authorities, since 1982, for the "monitoring" mission that the Soviets and the Western powers have been letting each other's military liaison teams perform in the two German states for almost 40 years. That much is not in contention.

There is a dispute over whether, when he was shot, he was in or merely near a restricted area. Our presumption is that the American side, which says he was not in a restricted area and was not doing anything outside the familiar terms of a time- tested liaison agreement, is telling the truth.

There is no dispute over the further American report that the Soviets did not allow Maj. Nicholson's driver to administer first aid to him and did not themselves tend to him until he had died.

Even if Maj. Nicholson had been in a restricted area, of course, the right and reasonable thing for the Soviet guard to have done would have been to warn him, perhaps to detain him, perhaps to take away his camera. But to kill him?

The right thing for the Soviet authorities to have done after the murder would have been to apologize and announce steps to establish accountability. Instead, they simply expressed regret at the death and then blamed the dead man for it, saying he had been caught spying. As in the KAL episode, their defensive blustering comments make a bad situation worse. As usual, they are attempting to recover by representing themselves as the aggrieved party.

The liaison missions are a form of authorized espionage whose useful purpose is to keep nerves and armies steady on both sides of a line that is the most heavily militarized front in the world. The missions give each side the confidence of knowing a bit more about what the other is doing, and since the Soviet Union as well as the United States benefits from the arrangement, the incident is doubly shocking. Once again the Soviets have demonstrated their proclivity to kill first and question later. There is no excuse or justification for it.

President Reagan is without illusion about this Soviet trait, so as each incident comes along he does not feel under pressure to change his foreign policy in order to show that he is without illusion. The Geneva negotiations go on, as they should. But the Soviets should understand the rage they have stirred by the killing of Maj. Nicholson, and the fresh political damage they have inflicted on the prospects for the improved relations they profess to seek.