THE RESIGNATION of Robert L. Green as president of the University of the District of Columbia brings to an end a shabby affair that should never have happened. It was right for him to go; he had abused his office and was tarnishing the school. He suggested in his statement of resignation that the media hounded him out of office, brought him down unfairly. Not so. The record ought to stay clear on that.

Plainly the important thing now is the choice of a successor. UDC and its predecessors have had trouble in picking and keeping presidents. The first president of Federal City College lasted about a year; that was about how long Dr. Green's own predecessor, Benjamin Alexander, lasted.

The job of running UDC ought to be one of the most exciting in U.S. education. It is obviously a school on the cutting edge of an important part of higher education, an open-enrollment university in a black-majority city. The need is enormous. A conscientious and creative president should be able to take the young school in all kinds of promising directions. Can it be there is no one out there like this? The board, a majority of whose members is appointed by the mayor, has struck out twice in a row. Perhaps it should look for someone other than a professional educator for a change. We don't know. We just know what it has done so far hasn't worked. The mayor kept his distance from the problems of Dr. Green. That may be understandable. Now he too should become involved, help at least to work out the selection process, accept some responsibility.

UDC is important to a lot of young people in this city. It is their ticket upward. Not enough who begin graduate. There are still arguments over standards at the school, still divisions from the merger with which the school began. Are these going to be allowed to last forever? The older people who have been running the school have failed the younger for whom the institution exists. This time they ought to do it right.