Fractal image coding (FIC) can exploit redundance at different scale in spatial domain. But there is no scheme presented to exploit the different scale redundance in frequency domain. In this paper, we extend the H product defined by Kou et al. Using the extended product, a new transform is constructed to exploit redundance at different scale in frequency domain. Meanwhile, a quantization method is proposed for the new transform. At last a new coder is constructed based on the new transform and quantization method. Experimental results suggest that the coder based on our transform can achieve better decoded image quality than FIC and JPEG, and the coding time of our coder is shorter than FIC.