Mutual information-based image registration has been verified to be quite effective in many clinical applications. However, when calculating the mutual information between two working images, we need to estimate the grey values of the transformed image by interpolation on the reference image, which introduces regular artefacts in the registration function. In this paper, we analyse the underling mechanism of the artefacts, and present a new statistical interpolation, which will not introduce new intensities. In addition, it also breaks the conformity of the interpolation points, which is considered as a major contributing factor to the artefacts in commonly used interpolations. These characteristics make the registration function much smoother, enabling easier convergence to a global extreme. Experimental results on clinical images verify these advantages.