Image-based visual servoing has been found to give satisfactory accurate and robust results. However, sin- gularity and local minima may appear causing stability and convergence problems. In this paper, we present new control schemes based on Halley's method as a temptative to obtain a robust system even when the desired configuration is singular. The new control scheme use the first and the second order derivatives of the error to be regulated to zero. Hessian matrices of an image point are thus determined to be used in the control schemes. Preliminary experimental results obtained on a 6 dof eye-in-hand system shows that a more accurate positioning can be obtained compared with classical methods.