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We report measurements and analysis of magnetization, resistivity and thermopower of polycrystalline samples of the perovskite-type Co/Rh oxide La$_{0.8}$Sr$_{0.2}$Co$_{1-x}$Rh$_x$O$_{3-��}$. This system constitutes a solid solution for a full range of $x$,in which the crystal structure changes from rhombohedral to orthorhombic symmetry with increasing Rh content $x$. The magnetization data reveal that the magnetic ground state immediately changes upon Rh substitution from ferromagnetic to paramagnetic with increasing $x$ near 0.25, which is close to the structural phase boundary. We find that one substituted Rh ion diminishes the saturation moment by 9 $��_B$, which implies that one Rh$^{3+}$ ion makes a few magnetic Co$^{3+}$ ions nonmagnetic (the low spin state), and causes disorder in the spin state and the highest occupied orbital. In this disordered composition ($0.05\le x \le 0.75$), we find that the thermopower is anomalously enhanced below 50 K. In particular, the thermopower of $x$=0.5 is larger by a factor of 10 than those of $x$=0 and 1, and the temperature coefficient reaches 4 $��$V/K$^2$ which is as large as that of heavy-fermion materials such as CeRu$_2$Si$_2$., 8 pages, 6 figures, accepted to Phys. Rev. B