An efficient and stable method of searching for optimum structures of molecules containing cyclic parts is proposed, where both the Cartesian and the internal coordinates are improved independently at each iteration of the optimization, and are used for the next geometry of the cyclic parts and of the remaining parts, respectively. The utilization of the Cartesian coordinates at the cyclic parts avoids the disastrous and irrecoverable distortions, which frequently occur if one uses the internal coordinates. For the remaining parts, the internal coordinates are used, so that an efficient calculation is obtained. The present method is tested in the search for the geometries of pyridine and ethylene oxide in the ground state and compared with the usual methods which employ either the internal coordinates or the Cartesian coordinates as optimization variables; the authors' method is found to be more efficient and more stable than the usual methods.