Her aides say she has "matured." Her onetime-ally-turned- enemy, George Dunne, president of the Cook County Board, is unkind enough to suggest publicly that she has been "sedated."

Mayor Jane Byrne insists that "nothing has changed. . . . I'm exactly the same."

Whatever the case, "the new Jane Byrne" has surged to the front of the slam-bang race for renomination in the Feb. 22 Democratic mayoral primary, the most fascinating political fight this city has seen since the 1950s.

In the first televised debate of the campaign the other night, Byrne's two rivals, Cook County State's Attorney Richard M. Daley and U.S. Rep. Harold Washington, ignored each other and focused all their fire on her. But she remained cool and poised, reinforcing the image of competent professionalism that has been established in the saturation television campaign by media consultant David Sawyer. A post-debate poll by the Chicago Sun-Times found Byrne rated the winner by 32 percent of the viewers, Washington by 21 percent and Daley by 17 percent, with the rest calling it even.

Four weeks before the voting, private polls reportedly show Byrne anywhere from 4 to 10 points ahead of Daley, who leads Washington by a similar margin.

Six months ago, the same polls showed Byrne badly trailing Daley, the eldest son and designated political heir of the legendary Richard J. Daley, who was mayor from 1955 until his death in 1976. But that was before Washington entered the race at the urging of fellow blacks, eager to flex the muscle of their expanded voter registration. And it was before Byrne began her Sawyer-guided political metamorphosis.

Four years ago, Byrne, who had been a minor functionary in the elder Daley's administration, pulled off a political upset over Daley's bland successor, Mayor Michael Bilandic. Her first two years in the big office on the fifth floor of City Hall were a series of explosions, marked by three major strikes of public employees and the abrupt firings or resignations of at least a dozen top aides. She feuded with everyone from press to presidents.

Politically, Byrne seemed to be greasing the skids for her own early exit. She backed Sen. Edward Kennedy in the 1980 Illinois presidential primary and shared in his humiliating defeat at the hands of President Carter. When young "Rich" Daley beat her handpicked candidate for state's attorney, Bryne's days seemed numbered.

But no longer. Bill Daley, managing his brother's campaign for mayor, acknowledges, "Obviously the intensity of dislike for Jane Byrne has diminished." Al Raby, Washington's campaign manager, says, "It's clear from all the polls that Mayor Byrne is the person to beat."

They--and everyone else--attribute the turnaround to the commercials Sawyer made and began airing as soon as last November's election was over. The ad blitz went essentially unanswered until Daley got his first spots on TV last week. Washington is still scrambling for money to begin his media campaign.

The Byrne of the TV spots is not the high-pitched, combative, chip-on-the- shoulder politician Chicagoans saw in the past, but a low-voiced, confident executive, talking about the challenges she has met. She says she has steered this city from a $1 billion deficit to a position of financial strength most other big cities would envy.

Her rivals challenge her description, claiming that Chicago has survived her mismanagement only by desperate short-term financial expedients. But her version is prevailing so far--and she stayed in character despite the shots her rivals took at her in the first debate, carried live to a huge audience by four of the city's television channels.

A tougher challenge faces her in the superior precinct organization Daley can deploy, drawing on his father's old 11th Ward machine and the mixture of Daley loyalists and anti-Byrne reformers around the city. If Daley splits the white vote evenly with Byrne, there is an outside chance that Washington might sneak in by mobilizing the same kind of big black vote turnout that astonished everyone in November and almost gave Adlai Stevenson an upset victory over Gov. James R. Thompson.

The bitterness in the battle is reflected in the campaign buttons around town reading, "Dump the Bitch, Vote For Rich," and the ill-concealed racism of some of the attacks on Washington.

In the code of Chicago politics, no quarter is asked--or given. But once again, it may be tough even for a Daley to beat City Hall.