Barbra Streisand shares the eerie warning Judy Garland gave her before dying of an overdose

• Barbra Streisand opened up about her friendship with Judy Garland in her new memoir "My Name is Barbra."
• Streisand said she and Garland became friends after their famous "Judy Garland Show" performance.

Barbra Streisand's new memoir "My Name Is Barbra" covers everything from her early years in Hollywood to her friendships with fellow A-listers, including Judy Garland.

According to Streisand, she and Garland became friends after Streisand was invited to perform a duet with the "Wizard of Oz" star on "The Judy Garland Show," in spite of made-up rumors that the two had a rivalry.

Streisand and Garland regularly spoke on the phone, and Streisand said Garland even came to one of the rare parties she hosted at her apartment in New York.

"I think she arrived late. And I remember her saying something I never quite understood: 'Don't let them do to you what they did to me,'" Streisand recalled of the eerie advice Garland gave her.

She continued: "I should have asked her what she meant, but I didn't want to appear too nosy."

Garland died of an accidental overdose in 1969, six years after she and Streisand performed on "The Judy Garland Show" together.

The "Funny Girl" star also shared details about her television performance with Garland. During their duet, they performed a medley of Garland's cover of "Get Happy," and Streisand's rendition of "Happy Days Are Here Again."

"I'll never forget singing that duet. We sat next to each other (me in my white middy blouse), and I noticed she was shaking. She grabbed my arm, as if to steady herself, and then clasped my hand and held on to it tightly," Streisand wrote.

"She never let go of me until the end of the song. I couldn't believe it. I thought, 'This is Judy Garland! Why is she frightened?'" the singer added.

According to Streisand, her "heart went out" to Garland, who struggled with her self-esteem and substance abuse throughout her career.

"Now, many years later, I understand. Somehow you become more scared as you get older," Streisand wrote. "And the more successful you are, the more the pressure increases… there seem to be more people out there just waiting for your to fail."