That´s not correct unfortunately, although it has been widely taught in economics text books, and you can blame Keynes for that. Keynes used that example to try and explain the process to parliament, and also to argue that the system didn't expand the deposit money supply over time. Ironically even the data (in the Macmillan report) he supplied contradicted him. It´s confusing as well, because the fundamental rules have changed over time.

Banks can lend up to an allowed multiple of their cash or equivalent reserves (gold standard regulation), and in the Basel era are also regulated on the ratio of their capital reserves to their loans. This acts to stop hyperflationary expansion, but there is a feedback loop between new deposits and new capital so the system does still expand slowly over time. This may be beneficial.

In engineering terms, Banks statistically multiplex asset cash with liability deposits, using the asset cash to solve FLP consensus issues that arise when deposits are transferred between banks. It´s actually quite an elegant system.