The effect of n = 1(2201) buffer layers on it = 2(2212) and n = 3(2223) thin films of Bi2Sr2Can-1CunOy was investigated to reduce the strain caused by the lattice mismatch between the films and the substrates. The bilayer thin films of 2213/2201 and 2212/2201 were grown epitaxially on SrTiO3 (100) substrates by de sputtering. When the thickness of the buffer layer was 10-25 nm, the superconducting transition temperature increased by similar to 20 K for 2223/2201 and by similar to 6 K for 2212/2201. The increase was attributed to the reduction of the strain from the experimental results of the full width at half-maximum of X-ray diffraction peaks, the length along the c-axis and the roughness of the film surface.