In this paper  new algorithm for  speeding up fractal image compression  is presented. A new adapted method based on computing the highest value of the pixel of the image to reduce the computational complexity in the encoder stage and which are led to decreasing the encoding time while the reconstructed image from the work as good as we want. For increasing the effectiveness of search stage we used another type of partitioning method that led to increase the flexibility of range partition, this method is HV-partition. We applied this method on images and also present a comparison of this method against other method which used to speed the fractal compression.