This letter demonstrates a novel optical single-sideband suppressed-carrier modulator design using a standard single-electrode Mach-Zehnder electrooptic modulator bidirectionally. It is proven that its single-sideband operation is insensitive to bias and optical modulation depth. Up to 25 dB of sideband suppression and 14 dB of optical carrier attenuation are obtained in experiments at microwave modulation frequencies. In addition, suppression of dispersion-induced power fading is demonstrated in a link with a total dispersion of 2691 ps/nm.