bat\ an\ eyelash

bat\ an\ eyelash
• bat an eyelash
• bat an eye
• without batting an eye
• without batting an eyelash
v. phr. informal
To show surprise, fear, or interest; show your feelings. - Used in negative sentences.

When I told him the price of the car he never batted an eye.

Bill told his story without batting an eyelash, although not a word of it was true.

Compare: straight face

Словарь американских идиом. — СПб., Изд-во "Лань". . 1997.