In this paper, we develop a model of money and reserve-holding banks. We allow for private liabilities to circulate as media of exchange in a random-matching framework. Some individuals, which we identify as banks, are endowed with a technology to issue private notes and to keep reserves with a clearinghouse. Bank liabilities are redeemed according to a stochastic process that depends on the endogenous trades. We find conditions under which note redemptions act as a force that is sufficient to stabilize note issue by the banking sector.