In this paper, we address the problem of hand-eye calibration of arobot mounted video camera. In a first time, we derive a new linear formulation of the problem. This allows an algebraic analysis of the cases that usual approaches do not consider. In a second time, we extend this new formulation into an on-line hand-eye calibration method. This method allows to get rid of the calibration object required by the standard approaches and use unknown scenes instead. Finally, experimental results validate both methods.