Quantitative easing (QE) as I understand it is the process whereby a central bank buys govt bonds in the open market (mainly from commercial banks), thus adding to the money supply. The commercial banks in turn, can use the multiplier effect to increase the money supply still further. Thus money is created in the economy.

That all sounds fine to me, but the banks had to have bought the govt bonds in the first place, so QE is simply putting money back into the economy that was there in the first place?

Can anyone please clarify?