The present invention related to a method of manufacturing a polycarbonate including the process of copolymerizing epoxide compound and CO2 using cobalt(III) or chromium(III), where the ligands contains at least 3 ammonium cations, central metal has formal −1 charge, and conjugated anions of the two cationic ammonium groups are acid-base homoconjugation, as catalyst.According to the present invention, the initial induction time can be reduced when the said polycarbonate is manufactured and it is possible to improve the activity of the catalyst and the molecular weight of the obtained polymer.