The reconstruction of shape and impedance obtained from measurements of scattered electromagnetic fields is considered for the two-dimensional case. Space mapping with inverse difference technique which is newly developed to solve inverse problem is used for this purpose. One of the advantages of this technique over other space mapping techniques is that it does not need parameter extraction during optimization process. As the contour of the cylinder is 2 pi periodic, it can be represented by Fourier series. Measurements of scattered field and Fourier coefficients of the contour are used as inputs and outputs, respectively. The results are compared with exact shapes, and good agreement is obtained. It is also observed that reconstructions obtained by space mapping based technique are better than those obtained by artificial neural network for exact and noisy data. Sharp cornered tetragonal contour is also investigated for both noisy and noiseless case in order to show efficiency of the technique.