The Earth climate system has an intrinsic mechanism to maintain its energy conservation by impelling opposite changes in meridional ocean and atmosphere heat transports, in response to climate change or variability. This mechanism is briefed as the Bjerknes compensation (BJC). We set up a global coupled two-hemisphere box model in this study, and obtain an analytical solution to the BJC of this system. In the two-hemisphere model, the thermohaline circulation is interhemispheric and parameterized by the density difference between two polar boxes. The symmetric poleward atmosphere heat and moisture transports are considered and parameterized by the temperature gradient between tropical and polar boxes. Different from the BJC in the one-hemisphere box model that depends only on the local climate feedback, the BJC here is determined by both local climate feedback and temperature change. The asymmetric thermohaline circulation leads to a better BJC in the Northern Hemisphere than in the Southern Hemisphere. Furthermore, an analytical solution to the probability of a valid BJC (i.e., negative BJC) is derived, which is determined only by the local climate feedback. The probability of a valid BJC is usually very high under reasonable climate feedback, which is also found to be robust in the real world based on observational data, implying that the Earth climate system maintains it energy balance very well during the past one hundred years.