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This paper presents a novel approach to incorporate the non-stationarities characterised in the GCM outputs, into the Predictor-Predictand Relationships (PPRs) in statistical downscaling models. In this approach, a series of 42 PPRs based on multi-linear regression (MLR) technique were determined for each calendar month using a 20-year moving window moved at a 1-year time step on the predictor data obtained from the NCEP/NCAR reanalysis data archive and observations of precipitation at 3 stations located in Victoria, Australia, for the period 1950–2010. Then the relationships between the constants and coefficients in the PPRs and the statistics of reanalysis data of predictors were determined for the period 1950–2010, for each calendar month. Thereafter, using these relationships with the statistics of the past data of HadCM3 GCM pertaining to the predictors, new PPRs were derived for the periods 1950–69, 1970–89 and 1990–99 for each station. This process yielded a non-stationary downscaling model consisting of a PPR per calendar month for each of the above three periods for each station. The non-stationarities in the climate are characterised by the long-term changes in the statistics of the climate variables and above process enabled relating the non-stationarities in the climate to the PPRs. These new PPRs were then used with the past data of HadCM3, to reproduce the observed precipitation. It was found that the non-stationary MLR based downscaling model was able to produce more accurate simulations of observed precipitation more often than conventional stationary downscaling models developed with MLR and Genetic Programming (GP). [ABSTRACT FROM AUTHOR]