This paper presents a network model of financial flow of funds accounting which can be used to calculate reconciled values of all outstanding financial instruments, tangible assets, and net worth. The model captures the accounting identities which must hold and permits the estimation of sector holdings of both assets and liabilities, as well as total outstanding instrument volumes. A decomposition algorithm is then developed which resolves the network problem into simpler subproblems proach of which can then be solved exactly and in closed form. A theoretical analysis of the algorithm is also given. Finally, the algorithm is applied to a dataset derived from the Federal Reserve Board data for 1989. The balanced dataset can then be used as a baseline for an empirical general equilibrium model.