The paper presents a method for estimating the control matrix in visual servoing using approximation up to the second order of the projection function. The classical approach simply uses the first order terms (inverse of the interaction matrix). The resulting control matrix is shown to perform much better than the classical one. Peculiarly, translation are made almost completely independent of z rotations, allowing better spatial trajectories. Theoretical insight as well as comparisons in the domain of visual servoing are provided to demonstrate this assertion.