SEOUL, South Korea — Two sisters accused of abusing Korean Air employees will be removed from management positions in their family-run corporate empire, the company announced on Sunday, four years after one of them became notorious for an episode of “nut rage.”

The executives, Cho Hyun-ah, 43, and Cho Hyun-min, 35, have become lightning rods for South Koreans who say that leaders of the family-run conglomerates known as chaebol, which dominate the country’s economy, often act as though they are above the law.

Cho Hyun-ah became infamous in 2014 when, as a Korean Air vice president, she flew into a rage after she was served macadamia nuts in an unopened package, rather than on a plate, in first class. Officials said she threw documents and insults at members of the flight crew and ordered flight attendants to kneel and beg for forgiveness.

Ms. Cho then ordered the Korean Air plane back to its gate at Kennedy International Airport in New York so that she could have the chief flight attendant removed.