The news came after a surprising dance-off, which saw Max and his partner Dianne Buswell compete against Maisie Smith and Gorka Marquez.
Max and Dianne had landed second from bottom after the judges' scores following their American Smooth to It Had to Be You by Harry Connick Jr, but were lauded last week for their Simpsons-themed Couple's Choice routine.
Maisie and Gorka, meanwhile, were fifth on the leaderboard after their Cha Cha to Girls Just Want to Have Fun by Cyndi Lauper.
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Both pairs performed again and then the judges – including Anton Du Beke, who was filling in for Motsi Mabuse – made their decision.
Craig Revel Horwood chose to save Maisie and Gorka.
He said: "Both couples were more concentrated and both couples took the notes we had given them and showed improvement. But the couple I'd like to save, Maisie and Gorka."
The bottom two couples were a surprise
Anton Du Beke agreed, saying: "Well, I have to say it's so close.
"They were both immaculate through that dance. It literally was just the smallest timing. For me, I'm going to have to save Maisie and Gorka."
Head judge Shirley Ballas didn't need to cast a deciding vote but said that she would have saved Max and Dianne.
When asked by co-host Tess Daly about his time on the show, Max said: "I've loved it. It's all down to Dianne, she's been literally amazing.
Max and Dianne were full of praise for each other
"For me to get through 90 seconds of a dance for four weeks now is a credit to her, she's just unbelievable."
Dianne also had kind words for her 2020 partner, saying: "I think Max has done an absolutely amazing job.
"He has done four incredible dances and I know how nervous you get, but you've come out here every week… you've done me more than proud - so well done."
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