A new rational bi-quartic spline interpolation scheme is constructed in this study. This rational bi-quartic spline has six free parameters that can be used to refine the final interpolating surface. The degree of smoothness attained is C1 continuity. Image interpolation is one of the methods in image processing that is used to rescale the images, either downscaling or upscaling. The proposed rational bi-quartic spline will be used to interpolate the missing pixel in image interpolation. We employ an algorithm that will speed up the process as well as be able to produce the quality upscaling images. We measure the quality of the proposed method by calculating peak-signal-to-noise-ratio (PSNR). Based on numerical comparison, the proposed scheme gives higher PSNR (consequently smaller RMSE) unlike some existing schemes. Thus, the new rational bi-quartic spline with six parameters is better than the existing scheme via an efficient algorithm. All numerical simulations and graphical results are presented using MATLAB. © 2013 IEEE.