I am with the ANZ. Being of advanced years I have been mortgage-free for a number of years. I recently purchased a new home and was able to pay a $35k transfer via Internet Banking, then to transfer $750,000+ to my lawyers trust account as a pre-arranged transfer also through Internet Banking. For the second transfer I was on the phone to the bank, they created the transaction for me to preview with Internet Banking and I then pushed the 'submit' button on, all while on the phone to them. The important feature was that I could review both the amount and the from/to account numbers as part of a normal IB payment (ie on my monitor).
So, with a bit of pre-arrangement with your bank, anything is possible.
I have a Serious Saver account that will never again have so many zeros in the 'balance available' amount.