I think Jerbourg is right. From what I remember Business Air became British Midland Commuter. British Midland Commuter were rebranded to British Midland Regional (on SAAB A340's (correct me if I am wrong)).
British Midland then spent millions and some bright spark thought up bmi - I would have only asked £100
!!
British Midland Regional became bmi regional who really came into their own sometime in 2003 with their own Air Operators Certificate.
If I got this totally wrong then please enjoy the laugh at my expense - I will.
