In this paper a control strategy for a redundant PUMA robot is presented. This robot is obtained from the conventional PUMA robot by addition of a joint parallel to the elbow joint. For redundancy resolution the following approach is chosen. From the position and pointing direction of the end effector of the PUMA robot the position and orientation of the fourth link of a 4R-manipulato? is calculated and the redundancy is resolved for this manipulator. This is done by adding an equation to the relationship between the joint angles and position and orientation of the fourth link. By this approach a control strategy is derived that allows motions of the end effector of the PUMA robot in a large part of its work space and shows repeatable behaviour. Furthermore, the redundancy is utilized so that the fiexture of the wrist is kept small.