It is proven that, if for any positive time T, there exists an open-loop control u(a, t) depending continuously on the initial data a, vanishing for a = 0, and steering a small neighborhood of 0 into 0 in time T, then the control system can be locally stabilized in small time by means of continuous time-varying feedback law, provided that the dimension of the state space is at least 4 and the strong accessibility rank condition holds.