Any flat fee brokers?

Here is a really newbie question. Assume for a second that I have millions (yeah, right) and want to trade forex. It would make sense for me to decrease my transaction fees as much as possible. For example, what if I wanted a flat fee on large transactions, rather than the x number of pips (which is I think like a percentage of our trade, since the fee gets bigger with the trade size). Are there any brokers that would cater to such an investor that wanted flat fee trades?

Thanks.