about bluetooth

can I turn off imac to always search the bluetooth device?

I have 2 mac in office, one keyboard paired in Mac #1

But after few month I unpair  and paired to my Mac # 2, all working fine.

But this month suddent mac # 1 alwys search out the mac# 2 keyboard and asking for pair always... (mac#1 have buy a new keyboard few month ago)

Now, I only can do is unplug battery in mac#2 keyboard.

anyone have idea?