New metal-ordered manganites RBaMn2O6 can be classified into three groups based on the structural and electromagnetic properties measured. The first group (R = Tb, Dy and Ho) shows three successive phase transitions, namely, structural, charge/orbital order (CO) and antiferromagnetic order (AF) transitions on cooling, as observed in YBaMn2O6. The second group (R = Sm, Eu and Gd) exhibits a CO transition, followed by an AF transition. The third group (R = La, Pr and Nd) exhibits a metallic ferromagnetic transition, followed by an A-type AF transition in PrBaMn2O6 and NdBaMn2O6. Compared with metal-disordered (R(0.5)(3+)A(0.5)(2+))MnO3, RBaMn2O6 has two remarkable features: (1) the high CO transition temperature (Tco) above 340 K and (2) the presence of a structural transition above Tco in the first group. These are closely related to the structural feature that the MnO2 sub-lattice is sandwiched by two types of rock-salt layers, RO and BaO, with different lattice sizes.