An efficient approach is presented for solving the inverse Jacobian problem for wrist-partitioned robots; specifically, the differential inverse kinematics problem. By selecting the wrist coordinate frame as the reference coordinate frame, a simplified Jacobian relation can be obtained for deriving a set of orthogonal bases for the screw system. From these orthogonal screws, the instantaneous Cartesian motion can be separated into translational and rotational parts for solving the differential joint variable rates. As a result, a set of concise, closed-form equations for solving the above inverse problem can be easily generated. For illustration, PUMA 560 robot is selected as an example. Based on the simplified equations, the exact form of the inverse Jacobian matrix can also be obtained.