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The actor wrote a message on his official website in memory of Courtney, who played The Brigadier on the BBC sci-fi show.
"Of all the characters in Doctor Who there is no doubt that he was the most loved by the fans for his wonderful portrayal of the rather pompous Brigadier," Baker said.
"'Five rounds rapid' was the line we all loved, always addressed to Sergeant Benton. Nick's close friends simply adored him."
He added: "He was a wonderful companion and his friends would call each other or email to relate the latest little stories of a night out with the Brig... We shall miss him terribly."
