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Cork eased their NFL relegation worries with a 0-12 to 0-07 victory over Down at Pairc Ui Rinn.
Eamonn Burns’ side, who needed to win to have any chance of extending their stay in the top flight, return to the second tier after just one season in Division One following last year's promotion.
Corl led 0-05 to 0-04 after a dire first half that saw just one point from either side from open play, although Down were indebted to goalkeeper Michael Cunningham for a sharp save to keep out a low Mark Collins drive on 12 minutes, while the Cork half-forward shot wide six minutes later when handed a second goal chance.
However, Cork extended their lead to five points at the start of the second half with a brace of points from Nemo Rangers pair Luke Connolly and Paul Kerrigan, and Down were unable to get within four of Peadar Healy's side from then on, although it could have been closer had Cork goalkeeper Ryan Price not flicked Donal O’Hare’s effort onto the post.
Kerry closed in on qualification to the league semi-finals by beating Monaghan 1-17 to 1-9 at Clones.
In contrast, Malachy O'Rourke's men are facing a relegation crunch clash with Donegal in the final round of fixtures next Sunday after a fourth consecutive league defeat.
Monaghan now need to win by 11 points against Donegal next week to avoid relegation.
The sides went in level at the break at 0-06 to 0-06, but points from Paul Murphy, Colm Cooper (2), Alan Fitzgerald (2) and Kieran Donaghy gave the visitors momentum in the second half as Eamon Fitzmaurice's side took a 0-012 to 0-06 lead.
Perhaps the crucial period of play came in the three minutes up to the hour mark, as Darren Hughes scored a 57th-minute goal for the Farney County only for Kerry’s to respond with a David Moran penalty goal on the hour in between points from Donaghy and Donnchadh Walsh to extend the lead to eight points.
Monaghan's Dessie Mone was then sent off in the closing stages for two yellow cards.
Cooper finished the match with six points, his best return since he underwent cruciate and knee surgery last year.
Mayo survived a second-half Roscommon comeback to win 1-11 to 1-07 at Dr Hyde Park and dent the Rossies' hopes of making the semi-finals.
Mayo should save their top flight status next weekend with victory over Down, but Roscommon may need a point against Dublin to secure their last-four place.