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"I wasn't upset about it. I was disappointed about it.
But it's just my experience told me that wasn't going to be a situation that was going to work," he said.
Cleveland management blocked Schwartz from taking alternative coordinator positions this offseason, so he will sit out the 2026 season.
The Browns are unlikely to trigger his 2027 option, making him eligible to return next year.
Monken, who replaced Kevin Stefanski, said during his introductory press conference: "I didn't take this job because of Jim Schwartz.
I have a lot of respect for Jim Schwartz as I would hope he has for me. But I took it because of the players that are here."
Monken hired first-time defensive coordinator Mike Rutenberg, who plans to maintain an attack-minded 4-3 scheme.
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Schwartz began his NFL career with the Browns in 1993.