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The RAS method is used to update or regionalize a single matrix such that it conforms to new row and column totals. This paper presents a correction of the RAS method (CRAS) that uses cell variation distributions calculated from multiple matrices of different periods or different regions. After the solution of the regular RAS, an additional optimization problem is solved that produces the most likely cell-corrections to the regular RAS solution. To test the behavior of CRAS, several simulations with a time series of input-output tables for The Netherlands for 1968-1986 are made. They show that-in situations of structural change-applying CRAS improves the regular RAS estimate. The method will also be applicable to traffic, trade, and migration matrices. (copyright) 2009 Wiley Periodicals, Inc.