A class of function transformation with reference variables is proposed, and it is proved that the method can reduce the step ratio deviation of the sequence to a certain extent. The sufficient and necessary conditions for reducing the step ratio deviation of the monotonically increasing and monotonically decreasing sequences are given respectively. In order to ensure that the modeling accuracy is still improved after the reduction, the function characteristics of non-expanding relative error in the transformation reduction of function with reference variables are further studied. Finally, the ${\rm GM}(1,1)$ modeling method is used to build the model. The example verifies that this kind of parametric variable function transformation method has the characteristics of reducing without expanding the relative error, and can improve the short-term prediction accuracy.