A new method is proposed, in this paper, to magnify a portion of an image based on the fact that fractal attractor has details at every scale. The formulae for magnifying image portions with fractal method are deduced. The fractal codes, the coefficients of a set of contraction mappings, are determined by encoding the portion to be magnified. The fractal codes are then modified according to the formulae deduced in this paper, and the magnified image is obtained by decoding the modified fractal codes. A portion of Lenna image is enlarged by a factor of 8 at both horizontal and vertical directions with 2 methods respectively, one is the new method described and the other is pixel duplication. Experimental results show that the new method is good for partial image magnification with no block effect.