The 67-year-old actress posted a tribute on Instagram to Kelly, who died on Saturday aged 69.
"A warm aloha to my older sister, Kelly Lee Curtis. She passed away this morning. In her home. In nature. At peace.
"She was my first friend and lifelong confidant. She was jaw droppingly beautiful, and a talented actress. She played a mean game of hearts, collected turtles, loved her family, nature, music, thrifting, travel, Facebook, and Pokémon Go. She was proud of her Danish roots and Hungarian Jewish ancestry and was a devoted American patriot," she wrote.
"She will be remembered for her loving generosity, fierce opinions, endless curiosity, unique style, and her powdered, almond, crescent cookies at Christmas, hence her name, Auntie Cookie.
"Kelly always signed off any message or fare thee well with a Hungarian blessing…
"Isten Veled, God is with you. (sic)"
Kelly was the daughter of Tony Curtis and Janet Leigh, and like her sibling, she enjoyed significant success in the entertainment industry.
Kelly made her acting debut in the adventure film The Vikings, which also starred her mother and father.
The actress subsequently appeared alongside Jamie in Trading Places, the 1983 comedy movie that also starred Dan Aykroyd, Eddie Murphy, Ralph Bellamy, Don Ameche, and Denholm Elliott.
Kelly featured in Magic Sticks and the 1991 Italian horror film The Devil's Daughter, too, as well as making TV appearances in episodes of The Equalizer, Hunter, Silk Stalkings, Star Trek: Deep Space Nine, and Judging Amy.
Jamie and Kelly both faced accusations of nepotism early in their acting careers.
However, Jamie pushed back against accusations that she's a so-called nepo baby.
"I guarantee you, the fact that my mother was in Psycho was a determining factor that maybe that will get them a little extra publicity," she told CBS News in January:
"Now, did it get me to that final two? No, my auditions got me to the final two."
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