The circulation character of 500hPa climatic height fields in two hemispheres is investigated by using hemispherical climatic field intensity( I_c) and the improved scheme for spherical function analysis.The main findings are as the followings:1)the intensity of 500hPa hemispherical climatic height field of winter(Northern Hemisphere) is stronger than that of summer(Southern Hemisphere);the transition velocity of hemispherical circulation from winter to summer about the same in two hemispheres but the transition from summer to winter in Northern Hemisphere is more rapid than in Southern Hemisphere.2)The spherical function spectrum structure of 500hPa hemispherical climatic fields is simple,and the fields are mainly composed of ultra-long waves(0≤m,k≤3;m,k not equal to 0 simultaneously),specially of zonal spherical function(m=0),thus showing a low order and dimension on feature.3)The 500hPa climatic height field can be accurately fitted by using 20 important spherical function components(criteria byr_m,k^*≥0.05%) in Northern Hemisphere, but by using only 10 in Southern Hemisphere,that is to say,the spectrum structure in Northern Hemisphere is more complicated.4)The seasonal variation of 500hPa climatic height fields in Northern Hemisphere is more remarkable than that in Southern Hemisphere.