The effects of interchannel scattering of conduction electrons by the impur
ity and repulsion of conduction electrons at the impurity site on the two-c
hannel Kondo model are simultaneously considered in this paper. It is shown
that these two perturbations will substantially modify the usual local non
-Fermi liquid behavior of the two-channel Kondo model. With bosonization an
d unitary transformations we find that the system can be transformed into a
single channel Kondo model with anisotropy between longitudinal and transv
erse exchange couplings. Whatever for originally antiferromagnetic or ferro
magnetic isotropic coupling, the system always hows to strong-coupling limi
t, which exhibits local Fermi liquid behavior at low temperatures.