Three basic sub-problems of screw theory are acceptable for some particular configuration manipulators’ inverse kinematics, which can not solve the inverse kinematics of all configuration manipulators. A new sub-problem is presented and the inverse kinematics thereof is solved in this paper. Based on the extended sub-problem, a manipulator, the inverse kinematics of which can not be solved by the three sub-problems without the participation of the new sub-problem, is constructed. The inverse kinematics of the manipulator is solved with the help of the extended sub-problem。Therefore a close solution is gained. The sub-problem herein can be applied directly in the inverse kinematics of a manipulator, providing a new approach for the inverse kinematics of a general configuration manipulator.