A year ago this month, Sen. Howard H. Baker Jr. quit the race for the Republican presidential nomination. After four straight third- and fourth-place finishes in caucuses and primaries, the man most feared by many Democrats as a White House challenger shut down his campaign, telling reporters with unpitying candor, "It isn't going anywhere."

Today, the 55-year-old Tennessean surveys his domain as the first Republican majority leader of the Senate in 26 years and says, "I really enjoy the hell out of this job. It is pure delight."

There is every reason to believe that Howard Baker is as honest in appraising his present situation as he was a year ago. He was thrown his considerable intellectual and political skills into the task of shepherding the 53-member GOP majority. And, unlike those primary voters, both the senators and the president appear to appreciate the quality of Baker's effort.

"This is probably the most unified majority party in the Senate in decades," said one White House lobbyist, "You don't know what a help it is to us," said another presidential assistant, "to know that Baker's got the Senate in hand."

That was not the general assumption immediately after the November election. There was talk that moderate Republican Baker would have a hard time with the platoon of incoming freshman GOP senators, many of them conservative ideologues. There were rumors that he might be dumped in favor of Ronald Reagan's friend, Sen. Paul Laxalt (R-Nev.) or upstaged by Laxalt in dealings with the White House.

But Laxalt -- far from challenging Baker -- nominated him for majority leader in the GOP caucus, and there are fewer and fewer stories suggesting that anyone other than Baker is calling the shots for the Senate GOP.

The rambunctiousness of his flock was tested early. Conservatives despise voting for increases in the national debt limit, but the first request from Reagan was for such an increase. Despite the tooth-gnashing, Baker held all but three of his 53 votes in line for the president.

He is managing to inculcate among his novice legislators his personal ethic of responsibility in the exercise of power by being very sure that everyone is part of the act.

There are weekly lunches with rotating groups of four freshmen. Often, at the end of the lunch, Baker gets on his "hot line" -- a direct tie-line to Max L. Friedersdorf, the head of Reagan's congressional liaison staff -- to relay some freshman's request or signal a need for some White House attention.

Once a week, the Republican committee chairmen gather in his office to go over their agendas and vent their problems, with one of the freshmen (from a rotating roster) sitting in to share the learning experience. "It gives me a central role in managing the flow of legislation," Baker says, "and it gives all the committee chairmen an overview of the agenda, too."

The result has been a sense of teamwork among Republican senators of diverse views. When he needed help on the debt-ceiling vote, for example, Baker asked Sen. Strom Thurmond of South Carolina -- that symbol of conservatism -- to talk to the freshmen. "He told them he'd never voted in his life to lift the debt ceiling, but he was going to do it this year for Ronald Reagan -- and they were too," Baker recalled. "It was a damned effective speech."

Beyond such political satisfactions, what Baker enjoys is his growing identification as a Senate man. That does not mean he has ruled out another run for president someday. But it does mean that the view from his office window, looking down the Mall to the monuments and the hills of Arlington, is one he deeply cherishes.

The three-room suite he occupies was, he reminds visitors, the first part of the Capitol put to use. One room was the House of Representatives, one the Senate and one (now his conference room) was the Library of Congress. The 3,000 volumes that were once on its shelves were the books the British set to the torch when they burned the Capitol. But their titles are known from catalogs of the present Library of Congress, and Baker is joyfully engaged in raising a million dollars in private funds to have library copies rebound in 18th-century bindings and placed on replicas of the original Latrobe shelves.

As he talks of his restoration project while looking down the Mall, you can believe he really does think, as he says, "This is the second best view in Washington. Only the Rose Garden from the Oval Office tops it."