Can one user's account in a Mac be set to a different time zone from another account in the same Mac?

I was mildly surprised yesterday to find that when I experimented by
creating 
a second user's account and setting that account's time zone to GMT (=
UTC) 
my first account's time zone followed suit.

Is there a way to divorce one account's clock from another account's clock
in 
the one computer? Or is that a trick whose time will come to Cupertino all
in 
good time?

-- 
Arfur Moo