This article develops a general network model of financial flow of funds accounting that explicitly incorporates feedback and can be used to calculate reconciled values of all outstanding financial instruments, tangible assets, and net worth. The model captures, as special cases, distinct data-specific problem scenarios and permits the estimation of sector holdings of both assets and liabilities, total outstanding instrument volumes, and total sector holdings. A decomposition algorithm is then proposed that resolves the network problem into simpler network subproblems, each of which can then be solved exactly in closed form. The algorithm is applied to a dataset derived from the Federal Reserve Board data for 1989. The reconciled dataset can then be used as a base line for an empirical general equlibrium model and for macromonetary policy analysis.