By a generalization of the well-known extended Jacobian method for stationary manipulators, we derive the extended Jacobian inverse kinematics algorithm for nonholonomic mobile robots. Key points of the derivation consist in de. ning the kinematics of a mobile robot as the end-point map of a driftless control system, decomposing the space of control functions of this system into a finite and an infinite dimensional subspaces, and introducing an augmenting kinematics map subordinated to this decomposition. The original kinematics and the augmenting kinematics constitute the extended kinematics. The inverse Jacobian of the extended kinematics defines the extended Jacobian inverse kinematics algorithm. By design, the algorithm is repeatable. As an example, we derive a specific extended Jacobian inverse kinematics algorithm and illustrate its performance with the computer simulations.