In this paper we present a singularity free trajectory tracking method for the cooperative working of multi-arm robot manipulators. It is based on an inverse kinematic transformation which determines the manipulator's joint angles corresponding to the end-effector trajectory given in the task space. The kinematic problem of multi-arm robot system is solved by using screw theory and quaternion algebra. Screw theory is an effective way to establish a global description of rigid body and avoids singularities due to the use of the local coordinates. Dual-quaternion is the most compact and efficient dual operator to express screw displacement. Inverse kinematic solutions are obtained by using Paden-Kahan sub-problems. The proposed method is implemented using two Stubli TX60 robot arms and simulation results are given.