We propose a method to suppress the so-called zero-order term in a hologram, based on an iterative principle. During the hologram acquisition process, the encoded information includes the intensities of the two beams creating the interference pattern, which do not contain information about the recorded complex wavefront, and that can disrupt the reconstructed signal. The proposed method selectively suppresses the zero-order term by employing the information obtained during wavefront reconstruction in an iterative procedure, thus enabling its suppression without any a priori knowledge about the object. The method is analyzed analytically and its convergence is studied. Then, its performance is shown experimentally. Its robustness is assessed by applying the procedure on various types of holograms, such as topographic images of microscopic specimens or speckle holograms.