Eve Arnold took this picture of Marilyn Monroe on the set of The Misfits in 1960. Monroe’s husband Arthur Miller had initially written the movie for his wife to star in – opposite her teenage crush, Clark Gable ­­– as a Valentine’s gift, but by the time of the production, Miller and Monroe were close to divorce. Arnold had been invited on set to chronicle the making of the film, but she ended up documenting the end of a marriage.

The photographer had first met Monroe in 1952, and she helped to make her legend, photographing her in an airport bathroom with her skirt hitched up to her waist, and reading the Molly Bloom section of Ulysses in Central Park. This picture is included in a new exhibition of Arnold’s images of women, which takes in fashion shows in 1950s Harlem and her era-defining reportage for the Magnum agency. I interviewed the photographer in 2002, when she was 90, and she reminisced about Monroe, her muse and her friend: “She made me feel as if I were brilliant,” Arnold said, “and I suppose I made her feel as if she were brilliant. Actually we were two young women starting out in this quite male world, so we just played together, had the most fun we could.”

That fun was in fairly short supply on The Misfits, however. The film was shot in the 40C-plus heat of the Nevada desert. The director, John Huston, was drinking and gambling, and Monroe’s prescription drug addiction saw her frequently absent from the set and finally hospitalised for two weeks. “She was being atrocious to Arthur,” Arnold told me. “It began in the heat of the summer and ended in the cold of the desert. It was not a happy set, and it got less happy.”

• Eve Arnold – To Know About Women is at Newlands House Gallery, Petworth, Sussex, 1 July–7 January