NEW YORK -- A second arbitrator has ruled that NFL commissioner Roger Goodell has the authority to discipline four New Orleans Saints players for their roles in a bounty program.

The players' union claimed Goodell is prohibited from punishing players for any conduct before the CBA was signed last August. The union also sought to have player appeals heard by Art Shell and Ted Cottrell, who are jointly appointed by the league and union to review discipline handed out for on-field conduct.

But arbitrator Shyam Das ruled Friday that Goodell is entitled to hand out the punishment and hear any appeals in the matter.

In a statement released by the NFL, Das wrote that the provision waiver relied upon by the union "does not . . . constitute an agreement by the NFL that the Commissioner relinquishes authority to impose discipline for conduct detrimental occurring prior to the execution of the CBA on August 4, 2011."

It was the second victory for the NFL in grievances this week.

On Monday, Stephen Burbank, a University of Pennsylvania law professor, ruled that Goodell has the authority to discipline the players.

The NFLPA later said it would appeal Burbank's decision because it believes salary-cap violations are involved in the payment.

Goodell suspended Saints linebacker Jonathan Vilma for the entire 2012 season and teammate Will Smith for four games. Former Saints defensive end Anthony Hargrove, now with Green Bay, was suspended for eight games, while linebacker Scott Fujita, now with Cleveland, was docked three games.

Information from The Associated Press was used in this report.