The paper provides main lines for balancing the current estimates of Italian quarterly national accounts within a system of supply and use tables. In a first step, a preliminary estimate of change of inventories split by product is implemented. Then, based upon simplified assumptions, the commodity flow approach is expanded towards a full system of preliminary estimates of quarterly supply and use tables. Finally, these tables are balanced applying an algorithm able to respect both temporal and sectional constraints provided by the annual set of tables. The algorithm operates by product, setting a state space form of multivariate constrained regressions, whose statistical treatment is based upon the Kalman filer and smoothing. A pre- and post-balancing comparison of seasonal adjusted GDP components in volumes is presented.