A version of the Diamond-Dybvig model of banking is used to evaluate the narrow banking proposal, the idea that banks should be required to back demand deposits entirely by safe short-term assets. It is shown that the mere existence of an amount of safe short-term assets outside the banking system that exceeds banking system liabilities does not make the proposal either innocuous or desirable. In fact, despite such existence, using narrow banking to cope with banking system illiquidity eliminates the role of the banking system.