This chapter analyzes the Black-Fama-Hall (BFH) system and then the indexed unit of account. According to Cesarano, the basic feature of new monetary economics is a non-tangible means of payment with a separation of the medium of exchange from the unit of account. Using a Mengerian approach to new monetary economics, T. Cowen and R. Kroszner argue that media of account evolved prior to media of exchange and that assets used as media of exchange change over time in an ongoing process. The BFH system offers the possibility by defining the unit of account as a large, encompassing commodity bundle. The BFH system may create long-run price stability, by defining away inflation. The BFH system has indirect convertibility that pegs the price level, since it requires banks to redeem checks with an amount of gold, or some other redemption medium, giving arbitrage that reverses any deviation of the price of the bundle from its defined price.