This paper proposes an allocation scheme based on cumulative emission per capita to achieve a globally equitable carbon emission space. Within this scheme, each country has an equal cumulative emission per capita during the considered time period, and their annual emission per capita would reach the same level in the converged year. It is quantified by assuming a quadratic annual emission per capita for each country in the allocation interval. The country-specific emission trajectories are provided based on long-term targets, and then adjusted to strictly follow the global emission pathway. We analyze the peak years and associated abatement costs with different starting years under this scheme. Compared with three other schemes, this new allocation scheme considers historical emissions and future needs for developed and developing countries simultaneously. (C) 2013 Elsevier Ltd. All rights reserved.