Extinction of counterflow diffusion flames of air and methane diluted with nitrogen is studied by drop tower experiments and numerical calculation using detailed chemistry and transport properties. Radiative heat loss from the flame zone is taken into consideration. Experimental results identified two kinds of extinction at the same fuel concentration, that is, in addition to the widely known stretch extinction, another type of extinction is observed when the stretch rate is sufficiently low. Consequently, plots of stretch rates versus fuel concentration limits exhibit a "C-shaped" extinction curve. Numerical calculation including radiative heat loss from the flame zone qualitatively agreed with the experimental results and indicated that the mechanism of counterflow diffusion flame extinction at low stretch rates was radiative heat loss.