Regarding the carbon emissions allocation principles, whether historical responsibility can be and how to be incorporated into the global climate framework is still under heated discussions. Here we argue that the permits share of most developed countries will sharply shrink when historical responsibilities are taken in through our assessment and comparison of six selected allocation proposals. To find a more convincing way of responsibility shift, we modify the existing method by giving each participant an independent year, decided by comparing its economic development with reference to China, as the start point to calculate its own responsibilities quantified by the historical cumulative emissions. Then we obtain carbon emission accounts of 137 countries and regions on the basis of per-capita cumulative emissions. Compared with the conventional method, there is an average 2.5% increase in emission deficits of the U.S.A, Canada and Japan, however, a 50% decline in emission deficits of OECD Europe; emission revenues of China, India and Brazil decrease by 39%. This paper presents a systematic and quantitative method to achieve a common but differentiated responsibility shift, not only between developed and developing countries but also within industrialized countries, in the hope of providing the framework for rational allocation of carbon emissions to be deliberated in the forthcoming climate change program of the United Nations.