HOUSTON — The New York Mets took another step toward cutting ties with closer Francisco Rodriguez, announcing Tuesday night that the organization has placed him on the disqualified list and exercised its right to convert his contract to a non-guaranteed deal.

The Mets will not pay him during his time on the disqualified list and opened the door to terminating the contract completely. Rodriguez is due about $3 million for the remainder of this season and then $11.5 million next season. He has a vesting option of $17.5 million for 2012 that would kick in if he finishes 55 games next season and passes a physical after the season.

But this action would allow the Mets — if it holds up — to terminate the contract at their discretion. While it seems a long shot that the Mets can win a fight with the powerful Players Association, this shows just how determined the organization is to rid themselves of Rodriguez.

Rodriguez suffered a torn ligament in the thumb on his pitching hand during an alleged altercation with his girlfriend's father in the family lounge at Citi Field last week. He served a two-game stay on the restricted list, but after pitching Saturday, he told the team that he felt pain in the hand and underwent surgery Tuesday.