Fractal image coding techniques usually partition the input image into small range blocks. This artificially introduces boundaries into the image resulting in the unpleasant blocking artifacts in the decoded images especially at high compression rate. Because the effect is especially responsible for the restrictions of the block-based coders, the solutions must be sought to reduce this blockiness. Recently two possible schemes have been proposed by other researchers: One may try to use overlapping blocks in the fractal transform, and the other to employ the combined fractal wavelet approach. An alternative solution is proposed, which employs the bilinear interpolation techniques and the resolution independence of fractal coding, in the sense that an image can be decoded at higher or lower resolutions than the original. Experiments show that the proposed scheme can eliminate the blocking artifacts.