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The Buffalo Bills hoped that by setting Jairus Byrd free he might come back to them.

Byrd, among the most talented players available when then the NFL’s free-agency period began Tuesday afternoon, visited the New Orleans Saints and stayed there.

He signed a six-year deal worth $54 million, with nearly $28 million in guarantees, including an $11 million signing bonus.

“I first want to thank the Buffalo Bills organization and the great fans of Buffalo for their support during my time there,” Byrd said on the Saints’ website. “I think there are great things to come here in New Orleans, and I’m excited to join this team.

“We played against the Saints this year and I saw their style of play and was impressed by it. I think I will fit well in the scheme.

“This is a great opportunity to join a championship organization. I look forward to meeting my new teammates and being part of a great Saints defense.”

Byrd will be paired with Saints sophomore Kenny Vaccaro, forming one of the NFL’s most impressive safety duos for defensive coordinator Rob Ryan.

Byrd’s departure won’t be easy for Buffalo to overcome. He’s a versatile ball hawk. He went to three Pro Bowls under three head coaches and three defensive coordinators.

The Bills lost Byrd on Tuesday after declining to use their franchise tag on him a second straight season partially because General Manager Doug Whaley hoped the gesture would ease negotiating tensions.

Byrd was upset last year because the Bills denied him the opportunity to test the open market. He refused to sign his $6.916 million franchise tag until every offseason workout and training-camp practice was over.

The Bills certainly had that in mind, too, when declining to franchise him again this year. Byrd missed every preseason game and the Bills’ first five regular-season games with plantar fasciitis.

He still tied for the team lead with four interceptions. He recorded 48 tackles, a sack and a forced fumble.

When quarterbacks threw into his coverage, analytics site ProFootballFocus.com charted them for a 35.0 passer rating, second-lowest for all safeties behind Glover Quin of the Detroit Lions.

email: tgraham@buffnews.com