THE UNIVERSITY of the District of Columbia seems located at a perpetual square one. Every few years, another of its presidents is repudiated and his plans and vision rejected. Meanwhile, the university's problems drag on. These include the poor graduation rate of its students, the lack of a recognized and sensible academic niche, the embarrassment of its athletic program, and the fact that it is perhaps the only land-grant institution in the nation with so little land that it is forced to spend large sums from its budget on rent.

Right now, UDC's trustees say that they want a strong president who has experience in dealing with poorly educated, low-income students and who can gain the support of a new mayor and D.C. Council and the local business community. They want a respectable athletic program, and they plan a new push for a Mount Vernon Square campus.

But this agenda does not go to the heart of UDC's difficulties. The institution is attempting to be the only public university system in the nation that does not fully separate its two-year program as a community college from its four-year program as a university. UDC's board of trustees wants to lead a large number of inadequately prepared students toward a four-year undergraduate degree. That is a tall order. But at the moment it is only a policy statement, not a completed action plan. How will this goal be accomplished? Is it something that the new president will be expected to develop?

Perhaps more than anything, UDC's board of trustees, under Nira H. Long, desperately wants the university to be a national model in some academic specialty. Mrs. Long leans toward teacher training, even though relatively few UDC students appear interested in that field. This is the kind of question that should be addressed, at least partially, before the search for a new president gathers speed.

If the UDC community can offer explicit answers to questions like these, it stands a better chance of attracting applicants for president who are interested in similar ends. If it cannot, it risks discouraging candidates who could hardly be expected to trade a safe job for a murky situation. The best candidates will want to know not simply that they will be allowed to lead but where they will be expected to go. Anything short of that invites a return to a dismal square one.