This paper proposes a simple numerical technique for the steering of arbitrary analytic systems with no drift. It is based on the generation of "nonsingular loops" which allow linearized controllability along suitable trajectories. Once such loops are available, it is possible to employ standard Newton or steepest descent methods, as classically done in numerical control. The theoretical justification of the approach relies on recent results establishing the genericity of nonsingular control, as well as a simple convergence lemma.