We introduce a new approach to determine the normal of Earth's bow shock, based on four-point magnetic field measurements. The method obtains the local bow shock normal, based on the assumption that the normal is in the opposite direction to the gradient of the magnetic pressure or magnetic strength (within the shock front). This gradient can be deduced from the four-point magnetic field measurements of Cluster. Applying the method, we calculate the normal of the bow shock for 28 Cluster crossing events from March to April of 2002 and February to March of 2004 and compare the results for the boundary orientation to commonly known methods, i.e., minimum variance analysis and the coplanarity theorem. In addition, we compare results of the normal obtained by four spacecraft timing analysis, under the assumptions of local planarity and constant velocity of the boundary (triangulation). It is known that minimum variance analysis often fails because of the temporal variation of the bow shock and coplanarity analysis often fails because of the existence of an overshoot or poor determination of the downstream magnetic field due to plasma disturbance. We find that the gradient analysis agrees most closely with the timing analysis, and, in general, the shock orientations obtained fit the expected bow shock geometry. The gradient method is valid for quasi-stable shocks and does not require the conditions of coplanarity or constant velocity of the bow shock to be satisfied. Its accuracy depends on this stability and the relative spatial scale of the shock, which should be large compared to the spacecraft configuration. A feature of the method, however, is that it provides an estimate of the normal point by point in time, allowing the nature of the spacecraft sampling to be monitored in terms of behavior as each shock event is traversed.