Zaìjìan !

"Zài Jiàn" is more often used when the speaker or the one spoken to, is to be away for a certain length of time. It's perfectly normal to say " zài jiàn " on the phone, though it might still sound a bit odd when family members or people live under the same roof say " zài jiàn " when going to work, going to class or just going on some errands. " Zài jiàn " is somewhat less often used in non-putong hua environment for daily encounters, though it has already made way into most if not all vernaculars and it's now a standard word to say on this occasion.

Wave hand to say:  
Good-bye!

Chinese often wave hand, at times from a distance, to say good-bye at seeing-off, which would be mistaken at times for greeting as saying " hi! " by Westerners.