In this paper, a new canonical form, called extended non-holonomic integrators (ENI), is firstly introduced for nonholonomic systems. Next, a recursive design technique is presented to exponentially stabilize ENI systems. The relationships between the convergence rates of the states and the controller parameters are explicitly given, in particular, the convergence rate of individual state can be specified explicitly. Then, it is shown that non-holonomic systems in ENI form, chained and power forms are equivalent, thus can be dealt with in a unified framework. Finally, a car-like mobile robot is used to demonstrate the effectiveness of the proposed control.