An examination of quasi-perpendicular shocks (42.7¿≲&thgr;Bn≲88.3¿) using ISEE-1 and -2 fluxgate magnetometer data has shown that the magnitude of the magnetic field behind the shock front often overshoots, i.e., rises to significantly larger values than observed some distance downstream from the shock. Usually the overshoot is followed by an undershoot of comparable or longer duration and comparable magnitude before the normal magnetosheath values are reached. 110 shock crossings are examined. Only shocks with ratios of fast Mach number to critical Mach number. M/Mc, greater than 1 exhibited the overshoot. This suggests that the structure is associated only with supercritical shocks. The amplitude of the overshoot increased with M/Mc and, to a lesser degree, with solar wind ion &bgr;. No dependence of overshoot amplitude on &thgr;Bn was apparent. The thickness of the overshoot was found to be a fern ion gyroradii based on the solar wind velocity and magnetic field strength upstream of the shock.