Despite more than half a century of development, the Islamic finance industry is still an unfinished structure. This situation is related to the fact that the Islamic monetary authorities are building the Islamic finance industry on the foundation of traditional monetary relations, instead of creating a monetary system that meets the requirements of Sharia, that is, devoid of a credit component. The solution to the problem is proposed in the author's concept of the Islamic monetary system. The concept addresses the shortcoming (from an Islamic perspective) of traditional finance, where the category of "money" includes not only the functions of an exchange equivalent but also those of savings. The Islamic financial system proposes the following: a) the emission of money (for making purchases) and b) the emission of special financial tokens secured by a share of the assets of enterprises in a Muslim country (for saving). The article presents the rationale for two types of special financial instruments, their characteristics, and the implications of their use. The proposed monetary system design will help overcome the lack of short-term financial instruments in Islamic finance, which are essential for Islamic financial regulators to manage liquidity in the banking sector and for Islamic banks to organize the interbank lending market. It will also create a basis for determining the margin for several Islamic contracts, including murabaha and ijarah.