An improvement scheme, so named the Two-Pass Improved Encoding Scheme (TIES), for the application to image compression through the extension of the existing concept of Fractal Image Compression (FIC), which capitalizes on the self-similarity within a given image to be compressed, is proposed in this paper. We first briefly explore the existing image compression technology based on FIC, before proceeding to establish the concept behind the TIES algorithm. We then devise an effective encoding and decoding algorithm for the implementation of TIES through the consideration of the domain pool of an image, domain block transformation, scaling and intensity variation, range block approximation using linear combinations, and finally the use of an arithmetic compression algorithm to store the final data as close to source entropy as possible. We then conclude by explicitly comparing the performance of this implementation of the TIES algorithm against that of FIC under the same conditions, in which the TIES algorithm exhibits significantly better compression performance for large images (1024x1024px) compared to the FIC algorithm.