In China, waving hands means saying goodbye.

在中国，摇手表示说再见。

youdao

youdao

He left without saying goodbye.

他不辞而别。

《牛津词典》

(Speech) Fujii says the government is saying goodbye to an old concept of growth, a concept that relied on large investments on public projects, an idea that whoever is making money should make more money to help the economy.

VOA: standard.2009.10.27

He's sitting there saying goodbye to everybody.

和大家道别。

耶鲁公开课 - 死亡课程节选

But Valdano is adamant the club will not be saying goodbye to Beckham or Ronaldo.

BBC: SPORT | Football | Other European | Real rebuff Beckham rumours

We mourn as a nation because we know we are saying goodbye to a friend.

CNN: Final farewell for Edmund Hillary

We had grown close to them all and it was like saying goodbye to family.

NPR: Kate Nolan, WWII Combat Nurse