This study implements and tests a mathematical programming model to estimate interregional, interindustry transaction flows in a national system of economic regions based on an interregional accounting framework and initial information of interregional shipments. A national input-output (IO) table, regional data on gross output, value-added, exports, imports and final demand at sector level are used as inputs to generate an interregional IO account that reconciles regional economic statistics and interregional transaction data. The model is tested using data from a multi-regional global input-output database and shows remarkable capacity to discover true interregional trade patterns from highly distorted initial estimates.