Abstract: Since Barnsley presented the concept of fractal image compression, especially after Jacquin proposed a fully automatic image compression algorithm, fractal image coding has attracted a great deal of attention. A new trend is to combine fractal image coding with other image compression algorithms. Among them is to code only part of the image using fractal technique and represent the remaining part using other approaches. Based on this idea, partial fractal mapping is presented and its properties under different conditions are discussed. Some beneficial conclusions with respect to its feasibility are obtained. Also given are a framework for partial fractal coding and a new partial fractal coding scheme which can improve compression ratio while reducing encoding time.