A new Tc enhancement method, a combination of alloying of Cu- and Tl-system
and selective reduction for hole-doping has been developed for Cu(1-x)Tl(x
)Ba(2)Ca(2)Cu(3)O10-y (Cu1-xTlx-1223) system. The method is very effective
for the Tc enhancement up to 132 K for Cu1-xTlx-1223 and 126 K for Cu1-xTlx
-1234(x=0.4 similar to0.9). A new concept of band degeneration effect is pr
oposed as the Tc enhancement mechanism for a common optimum hole-doping in
every CuO2 layers.