We present what is to our knowledge a novel technique for efficient suppression of the zero-order beam inherent in light patterns projected via phase-only computer-generated holograms (CGHs). Encoding a CGH on a spatial light modulator (SLM) with a limited fill factor produces a disturbing zero-order beam at the optical axis. Here, we propose to derive a CGH, which includes holographic information to project a corrective beam that destructively interferes with the zero-order beam. The CGH for projecting arbitrary light patterns plus a corrective beam are derived using the Gerchberg-Saxton algorithm where the iterations impose both amplitude and phase constraints for the target field pattern at the Fourier plane. As proof of principle, we analyze the viability of the technique by simulating the performance when applied on a practical SLM with a limited fill factor, fixed number of phase-shifting pixels, and wavefront distortion associated with the surface roughness of the SLM. (C) 2007 Optical Society of America.