on your honour

Từ điển Oxford Advanced Learner 8th

on your ˈhonour idiom
(old-fashioned)
1. used to promise very seriously that you will do sth or that sth is true
•I swear on my honour that I knew nothing about this.
2. to be trusted to do sth
•You're on your honour not to go into my room.
Main entry: ↑honour_idiom