SO PRESIDENT CARTER has ended his elaborate seven-month search for a new director of the Federal Bureau of Investigation by getting the man he wanted in the first place, U.S. District Court Judge Frank M. Johnson Jr. of Alabama. It is fortunate that Judge Johnson, who declined the job last winter, changed his mind and made his interest known a few weeks ago. And it is obvious why Mr. Carter and Attorney General Griffin B. Bell quickly signed him up. After an intensive nationwide manhunt, the administration's search committee had recommended five candidates, any of whom would have been qualified for a number of top government posts. But none of the five seemed to offer just the right combination of distinction, ability and experience for the ultra-sensitive task of leading the troubled FBI.

The difficulties of search did dramatize how high the administration's standards were and how distinctive the new director should be. The head of the search panel, du Pont board chairman Irving S. Shapiro, wrote in June that the msot vital factor would be the "inherent qualities" of the nominee, his "strength, integrity and dedication to the nation's basic values." By that standard Judge Johnson is a good choice. During his 22 turbulent years on the federal bench, he has established a record of judicial firmness, fairness, personal courage and unwavering commitment ot constitutional rights. Time and again he has broken new legal ground, not only during the civil-rights struggles of the 1960s but also in protecting dependent groups such as prisoners and mental patients against official abuse or neglect. He has a sharp sense of both the proper limits of government and the responsibility of powerful institutions to treat citizens with decency and respect.

These are formidable assests for anyone charged with redefining the purposes and practices of the FBI. Judge Johnson's record on the bench does not, however, fully answer the question of whether he can really run the bureau - which involves not only establishing the priorities and rules, but also maintaining both tight discipline and good morale. Even his experience in Alabama, in cases no redolent of political infighting and intrigue, may not have prepared him to deal with the bureau's internal pressures and complexities. To make a real impact on the agency, Judge Johnson would have to be not only tough, but also remarkably well-informed - and would have to command the loyalty of veteran agents and newer employees alike.

The Senate confirmation hearings should provide more insights into Judge Johnson's approach to this challenge. At that time, too, the nominee will have the opportunity to set forth his concept of the FBI's future - what its new statutory charter ought to be; what counterintelligence mandate the bureau should have, and under what constraints; how much of its resources should be concentrated on fields such as organized crimeme and white-collar offenses, which the FBI has slighted in the past; and how its field structure and personnel policies should be overhauled. We look forward to learning Judge Johnson's thoughts on these and other questions, for the challenge facing him is not just how to keep the FBI under proper control, but also how to make it a more effective law-enforcement agency.