I went to my fireplace, lit a match, then held the note in my left hand while I set fire to it with the match in my right hand. Once it was aflame, I blew out the match and threw it away, then dropped the note into my fireplace to burn itself out. Or, at least, that was the plan. I then remembered an important point about Post-It notes: they are designed to stick to things, such as (say) your fingers. Normally I would use my other hand to unstick the note, except that the rest of the note (the bit I'd grip hold of) was now on fire. Eep! I could have blown out the flame, but fortunately I was able to shake it loose before it singed my fingers too much.
Anyway, something to bear in mind for the future: next time I'll stick the note to a poker.