Katharine Hepburn for LIFE magazine, 1968.

“Huh,” Hepburn snorted when asked to sit still for LIFE’s photographer and the picture on the cover of the issue. “I haven’t done that sort of thing since 1944. Me posing like a starlet? You must be really desperate. That’s funny. That’s very funny.” Grudgingly, she assented and arrived at the studio at the appointed time with her fold-up minibike, some sand-colored gabardine suits, a faded olive fatigue jacket her brother wore to World War II, black turtleneck sweater and a couple of perky, peaked caps. “I hate the yellow background,” she grumped. Click, click, click. She struck another stance and turned on a smile, or what she calls “my girl Scout look,” Click, click, click. Then, whipping off her jacket, she demanded: “Look, tell your editors I never do anything standard, and this is all the old bag would do.” Whereupon, Miss Katharine Hepburn, without so much as wrinkling her ladylike self and pinking only slightly, turned herself base over apex for fully two minutes, without wavering a fraction, stood on her head.