Angered over a leak last month of information that his National Endowment for the Arts intended to approve a controversial theater exhibit, Chairman John E. Frohnmayer put his computer experts to work sifting through reams of outgoing NEA telephone calls to nail the leaker.

On May 25, armed with the results of his sleuthing, Frohnmayer summoned his chief deputy, Dr. Alvin S. Felzenberg, showed him the computer readout and accused him of being the source of the leak (to our column). Felzenberg, in complete honesty, denied the charge. Frohnmayer gave him four days to confess. If he confessed, he could stay on the payroll a week or two to look for a new job. Otherwise, his desk would be cleaned out May 29. In either case, he was fired on evidence Frohnmayer called ''circumstantial.''

That rare glimpse into the sometimes brutal world of Washington power and politics looked to White House officials, who soon learned about it, like a witch-hunt President Bush did not need. Frohnmayer quickly got orders: Keep Felzenberg on the job for now. Jack Lichtenstein, Frohnmayer's spokesman, told us Felzenberg ''will stay until he gets another opportunity to serve the president.''

Frohnmayer's computer search for a leaker inside NEA never had a chance. The source of our column that angered Frohnmayer does not and never did work at NEA but was appointed by Bush to another high post in a different government agency. Moreover, Felzenberg's telephone call to us was nothing more than a response to our call to a competent NEA official. We simply sought details about the controversial theater exhibit that we knew was headed for approval at the NEA Council session in Winston-Salem May 12.

The rift is deep between Frohnmayer and Felzenberg, who was praised by The New York Times last month as having ''a passion for the arts, a fighting spirit and a political savvy . . . perfect for the job.'' But NEA sources told us that Felzenberg made a nuisance of himself to Chairman Frohnmayer. He kept warning him to get tougher on NEA funding for exhibits considered ''obscene'' on Capitol Hill, and not just by conservatives. Otherwise, he correctly counseled Frohnmayer, the NEA would be run over in a congressional revolt.

But Frohnmayer's political antenna is not turned on. One White House aide privately speculated that the chairman may view Felzenberg as a juicy candidate for right-wing scapegoat of the NEA's political problems, even though his warning about the gathering storm over the NEA has proven accurate. Felzenberg was a visiting lecturer at Princeton before Frohnmayer invited him here last winter. Before that, he ran former governor Tom Kean's New Jersey arts agenda for eight years, raising state financing of the arts from $3 million to $25 million a year.

Frohnmayer has not returned our calls, even though Lichtenstein intervened on our behalf. That suggests political insensitivity going beyond his effort to fire Felzenberg. Some at NEA, by no means hostile to Frohnmayer, worry about this insensitivity.

An example given us by one such insider is the chairman's hire of an outside public relations counsel named Robert Witeck, highly regarded as senior vice president and a key operative in the Washington office of Hill and Knowlton. Witeck told us he counsels the chairman on special public relations and political problems. He said he is on the payroll as a consultant at about $250 a day and works about four days a month. Lichtenstein is Frohnmayer's full-time PR executive.

When Frohnmayer first arrived here last fall, longtime NEA insiders were surprised when, quite innocently, he asked to put his wife Leah, a proficient and highly experienced arts expert, on the payroll. He valued her advice. When informed that would be a violation of the anti-nepotism law, Frohnmayer found part-time office space for her in his own office and in other space available on a temporary basis.

With Felzenberg now barred from performing any of his regular duties except for peripheral NEA work with foreign countries, his work load has been taken over by Salina Ottum, who came here from Portland, Ore., Frohnmayer's home town. She ran the Portland Arts Commission with a staff of five and a budget of $100,000; she now administers a budget of close to $200 million and a staff of several hundred.

But that does not end the saga at George Bush's NEA. The direct involvement of the White House suggests yet another dramatic turn for an agency riven by the culture clash between the world of art connoisseurs and the world of the taxpaying public.