To aid the performance of simulation analysis of complex water resource systems, designers require some means of developing exogenous or input variables. A recent technique, synthetic hydrology, uses the statistical characteristics of the record to provide parameters for a linear regression model. However, when applied to a large system, a bias is introduced into the analysis; this bias is eliminated by application of two linear transforms (i.e., an orthogonalizing transform or rotation of axes and its inverse). Details of the mathematical development are presented, together with a computational method and several applications.