Two high-speed image converter cameras and a 600 MHz digital analyser have been used to investigate electrical breakdown of SF$_6$ in a 20 mm point-plane gap at pressures up to 5 bar (5 x 10$^5$ Pa). Time-resolved records have been obtained of the schlieren image, the light emitted from the gap and the gap current during the development of impulse breakdown. It has been shown that the breakdown mechanism in a short gap in SF$_6$ is similar to that observed in atmospheric air gaps of several metres length. A primary corona is followed by the development of a hot leader channel which consists of a series of discrete steps. In this work it has been possible to time-resolve these steps and also to estimate the values of corona charge, leader diameter and step length. From the results obtained some insight has been gained into the mechanisms of leader formation in SF$_6$.