This paperstudiesthe effect of symmetry process on the compression parameters of thefractal image compression technique proposed by Jacquin.Two kinds of tests have been conducted. The first all kind of the symmetry operations [0-7] were taken; while the second tests were concentrated on studying the effect of the following parameters Block Size, Step Size, Domain Size on the probability distribution of symmetry operation. The results show that the higher value of PSNR and the lower value of ET occur atevensymmetry operation only, but compression ratio is not affected with symmetry process. Also the occurrence probability of even symmetry is more than odd symmetry for all compression parameters. This behaviour can be utilized to reducethe encoding time to 50% with preserving PSNR.