NEW YORK — NBA players rejected the league’s latest offer Monday and began disbanding the union, likely jeopardizing the season.

Billy Hunter said players were not prepared to agree to David Stern’s ultimatum to accept the current proposal or face a worse one, saying they thought it was “extremely unfair.” And they’re aware what this battle might cost them.

But it’s risky. The league already has filed a pre-emptive lawsuit seeking to prove the lockout is legal and contends that without a union that collectively bargained them, the players’ guaranteed contracts could legally be voided.

Stern, who is a lawyer, had urged players to take the deal on the table, saying it’s the best the NBA could offer and advised that decertification is not a winning strategy.

Players ignored that warning, choosing instead to dissolve its union, giving them a chance to win several billion dollars in triple damages in an antitrust lawsuit.

Derek Fisher, flanked at a press conference by dozens of players including Kobe Bryant and Carmelo Anthony, said the decision was unanimous. But there were surely players throughout the league who would have preferred union leadership put the proposal to a vote of the full membership instead.

Hunter said the NBPA was in the process of converting to a trade association and that all players will be represented in a class-action suit against the NBA by attorneys Jeffrey Kessler and David Boise – who were on opposite sides of the NFL labor dispute, Kessler working for the players, Boise for the league.