Traditionally, hand-eye calibration has been done using point correspondences, reducing the problem to a matrix equation. This approach requires reliably detected and tracked points between images taken from widespread locations. In this paper, we present a new approach to performing hand-eye calibration. The novelty of the proposed method lies in the fact that instead of point correspondences, normal derivatives of the image flow field are used. Firstly, two different small translational motions are made, enabling the direction of the optical axis to be computed from image derivatives only. Secondly, at least two different rotational motions are made, enabling also the translational part of the hand-eye transformation to be estimated. It is also shown how to compute a depth reconstruction from the information obtained in the hand-eye calibration algorithm. Finally, we discuss how to calculate the derivatives and present some experiments on synthetic data.