1.on the basis of 根据，在……的基础上
Our trade is conducted on the basis of equality.
2.for the better 好转,向好的方向发展
I trust that things will take a turn for the better in the near future.
3.on board 在船(车、飞机)上
We went on board Athens yesterday morning.
4.out of breath 上气不接下气
I ran to the theater all along and was out of breath.
5.on business 出差
I am here on business as opposed to a holiday.