We consider the stability of current sheets where a normal component of the field is present. It is well known that reconnection in such systems progresses orders of magnitude too slow to explain observations, even when full kinetic models are used. We consider here a new possible mechanism for fast reconnection in such systems. We consider the effect of the possible presence of velocity shear that can drive the Kelvin-Helmholtz instability (KHI). The effect of the KHI is shown to convert shear flow into compression flow that drives reconnection. Three scaling effects can be discerned in the simulations. First, the reconnection rate is directly controlled by the driving mechanism which is provided by the KHI. The result of this new mechanism is that fast reconnection can be achieved even in absence of anomalous resistivity. Second, the effect of varying the initial sheared flow along the main magnetic field direction enhances the reconnection process. Finally, the reconnection rate is insensitive to the value of resistivity.