************************************************************************* 71159 We are aiming to construct the local X-ray Temperature Function of the brightest clusters which can be usable for further investigation of cosmology. From ROSAT All Sky Survey, Reiprich & Boehringer (Co-Is of this proposal) compiled an X-ray flux-limited cluster sample which has the highest completeness ever achieved. By the ASCA observations proposed here, temperature measurements for the complete sample will be completed. Then we can construct the cluster temperature function with the highest accuracy, which will give a strong constraint on cosmological models. *************************************************************************