Animagi

[kangasboy]

No: HPFGUIDX 40592

I am sorry if this has already been brought up, but I don't 
remember it ever happening. .  .
I was re-reading Prisoner of Azkaban last night, and I noticed 
something strange. 
Towards the end, (on page 309) Lupin asks Harry "Tell me about 
your Patronus.", and Harry tells him about  the stag, and how he 
thought he'd seen his father, etc. Lupin replies by telling him 
"Your father was always a stag when he transformed". This 
"always" is interesting, as it seems to imply that everytime a 
wizard transforms,  s/he has a choice as to which form they take. 
If the "always" wasn't there, it would follow logically that each 
wizard has only one animagus form.
So what do people think? Does the wizard's choice influence 
their animagus form? Or is there only one, innate animagus 
form possible? 

Kangasboy