In this letter, the TM020 mode of a rectangular patch antenna is modified by partially loading a mu-negative (MNG) or double-negative (DNG) metamaterial block. With proper constitutive parameters and filling ratio, the electric fields at two radiating edges of the patch can be out of phase, and a broadside radiation pattern is achieved. A novel dual-band rectangular patch antenna loaded with a pair of conventional double-positive (DPS) and MNG metamaterial blocks is proposed as an application example of the modified TM020 mode. Good impedance matching and similar patterns with broadside radiation are achieved simultaneously at both operating frequencies with a single-layer single-patch fed by a single coaxial line. Simulation shows that the modified TM020 mode gives an efficient radiator with sufficient gain and very low level of cross polarization. Partial loading of a DNG metamaterial block is also discussed for some special dual-band applications.