Digital image correlation is a popular method for estimating object displacement in successive images. At the pixel level, displacement is estimated by maximizing the crosscorrelation between two images. To achieve subpixel accuracy, displacement estimation can be refined in the vicinity of the crosscorrelation peak. Among existing refinement methods, quadratic surface fitting provides a good trade-off between accuracy and computational burden. The purpose of this paper is to analyze the quadratic surface fitting method. It is shown that the quadratic surface fitted to the cross-correlation values in the vicinity of the cross-correlation peak does not always have a maximum. Then the conditions ensuring the existence of a maximum are analyzed. The reported results consolidate the theoretic basis of the quadratic surface fitting method for subpixel motion extraction.