The answer is unambiguously no. And the very absurdity of the question underscores the types of tactics to which the United Federation of Teachers is willing to stoop as it breaks with the administration over the Children First initiative. It’s something that might give the schools chancellor and Mayor Bloomberg pause as they exercise the authority that they gained with the blessing of the union in the school-control deal last year.

Last Monday, the UFT filed suit against Mr. Klein in his official capacity, leveling the accusation of “discrimination in employment on the basis of race and national origin.” The union’s justification for this is that, under Children First, 864 paraprofessionals — which the union says are “approximately two-thirds” African-American, Hispanic, or members of other racial minorities — will lose their jobs, while presumably white administrators will be hired. The union doesn’t believe that Mr. Klein is a racist. Its spokesman told The New York Sun yesterday that the union’s president, Randi Weingarten, “has never doubted the chancellor’s intentions.” But it seems to think it can conduct negotiations by other means, after having refused to offer the Bloomberg administration anything in the way of union givebacks to weather the city’s fiscal crisis.

The misfortune is that when a union like the UFT dumps this kind of trash, it poisons the well as regards serious race issues that warrant discussion about town. In the shadow of the UFT suit, the request for a “racial disparity study” of the 4,024 layoffs expected before the end of this fiscal year in June — made by the heads of 100 Blacks in Law Enforcement and of Blacks in Government, along with the former head of the New York Civil Liberties Union, Norman Siegel — took on an unfortunate tinge.

The mayor’s spokesman, Jerry Russo, on Sunday denounced the activists who had made the request earlier that day as “dis gusting race-baiters.” This seemed to follow a new Bloomberg administration policy of responding with uncharacteristic harshness to attacks concerning racial issues. On the radio on Friday, the mayor called the UFT suit “the most outrageous thing,” and said, “That doesn’t help anybody.”

Thus has the debate sickened. As our Errol Louis wrote on the opposite page yesterday, there is a serious problem with racial segregation in city government, where there is a fire department that is 94% white and a Human Resources Administration that is overwhelmingly black and Latino. Mr. Louis argued that the mayor ought not bury his head on this issue, but talk to those asking to meet with him and discuss ways of desegre gating the city’s workforce. If that were accomplished, the city wouldn’t run into the same wall every time necessary layoffs are made. Yet who can blame the mayor and his administration for putting up the defenses when under attack from a teachers union that is manipulating the race issue to try to avoid any layoffs.

Perhaps the UFT would rather see some teachers laid off — about two thirds are white in New York City. But we all know it’s not a question of race; it’s a question of jobs and money. And playing the race card won’t change that. In the meantime, the Bloomberg administration has little reason to trade barbs with the UFT. It can simply express confidence that it will prevail in court on the merits. To prove discrimination requires evidence of intent, which is sure to be absent here — something Ms. Weingarten, an attorney by training, surely knows. With the union prepared to play dirty, perhaps there is reason to hope that Mr. Klein will eventually make the move that the unions most fear and that would bring the most benefit to minorities in the city over the long run: busting the Tweed Trust by introducing vouchers.