This paper introduces a new lossy approach for compression of cartoon images. The image is firstly partitioned into regions of roughly the same colour. The chain codes are then determined of all regions. The sequence of the obtained chain code symbols is transformed with the Burrows-Wheeler Transform, Move-To-Front transform, and compressed with Run-Length Encoding. In the final step, an arithmetic encoder may be used to compress the obtained binary stream additionally. The proposed algorithm is asymmetric, meaning that the decompression does not reverse all the steps of the compression procedure. The experimental results have shown that the described method produces considerably better compression ratios than JPEG, JPEG2000, WebP, SPIHT, PNG, and two of the algorithms specialised in compression of cartoon images: the algorithm using quad-tree, and RS-LZ algorithm. August small regions. Another lossless compression method, named RS-LZ, was developed by Li et al. [9]. The method uses the Freeman chain code in eight directions (F8) to represent the borders of the solid regions, and encodes pixels that are contained neither on the border nor inside of the solid region. Because of that, images containing a lot of small solid regions and images, where edge smoothing or JPEG-like compression has been applied before, are not compressed well. A promising research was done by Taylor in 2011 [18]. He introduced a lossy compression algorithm, which takes into account small colour differences between neighbouring pixels, and a quantization procedure for small details/noise. The algorithm owns a good compression ratio at the expense of losing some image information.A new lossy method for cartoon image compression, named Chain Code Cartoon Compression (4C), is proposed in this paper. The main novelty of this work is fulfilling the gaps in cartoon image compression by developing a new approach, which would outperform the state-of-the-art general-purpose and domain-specific algorithms. The proposed method firstly divides the image into free-form regions having similar colours. The shapes of the regions are described with chain codes, which are then transformed with Burrows-Wheeler and Move-to-Front transforms. The obtained stream of chain code symbols is then encoded with Run-Length Encoding and arithmetic coding. As the algorithm is asymmetric, the decompression is faster than the compression. For cartoon images, the proposed method produces better compression ratios than the referenced algorithms. Images compressed with the proposed method are also more visually pleasing than those compressed with JPEG, JPEG2000, WebP, or SPIHT, with approximately the same structural similarity index (SSIM). In most cases, the same SSIM of two images means that they are of the same quality. PSNR is also considered of decompressed images obtained with the mentioned algorithms.This paper contains 4 sections and an Appendix. The proposed compression algorithm and its steps are presented in Section 2. The third Section contains the results of the ...