The global climate change issue has the highest priority on the current agenda of the World community because of the global warming trend during the 20th Century. Conventional theory of global warming states that heating of atmosphere occurs as a result of accumulation of anthropogenic CO2 and CH4 in the atmosphere. The writers show that rising concentration of CO2 should result in the cooling of climate instead. The methane accumulation has no essential effect on the Earth's climate. Even significant releases of the anthropogenic carbon dioxide into the atmosphere do not change average parameters of the Earth's heat regime and the atmospheric greenhouse effect. Thus, accumulation of small additional amounts of carbon dioxide and methane in the atmosphere as a result of anthropogenic activities has practically no effect on the Earth's climate.