Orthorhombic rare-earth trivalent manganites RMnO3 (R = Er-Lu) were self-doped with Mn to form (R0.667Mn0.333)MnO3 compositions, which were synthesized by a high-pressure, high-temperature method at 6 GPa and about 1670 K from R2O3 and Mn2O3. The average oxidation state of Mn is 3+ in (R0.667Mn0.333)MnO3. However, Mn enters the A site in the oxidation state of 2+, creating the average oxidation state of 3.333+ at the B site. The presence of Mn2+ was confirmed by hard X-ray photoelectron spectroscopy measurements. Crystal structures were studied by synchrotron powder X-ray diffraction. (R0.667Mn0.333)MnO3 crystallizes in space group Pnma with a = 5.50348(2) Å, b = 7.37564(1) Å, and c = 5.18686(1) Å for (Lu0.667Mn0.333)MnO3 at 293 K, and they are isostructural with the parent RMnO3 manganites. Compared with RMnO3, (R0.667Mn0.333)MnO3 exhibits enhanced Néel temperatures of about TN1 = 106-110 K and ferrimagnetic or canted antiferromagnetic properties. Compounds with R = Er and Tm show additional magnetic transitions at about TN2 = 9-16 K. (Tm0.667Mn0.333)MnO3 exhibits a magnetization reversal or negative magnetization effect with a compensation temperature of about 16 K.