Paleomagnetic data frequently display bipolar data that are not exactly antipodal. One cause of this biasing is the addition of another later (secondary) magnetization that cannot be removed by laboratory demagnetization experiments. The magnitude of this hidden secondary magnetization can be calculated when only two values are known: the non-antipodal angle (measured), and the angle between the Normal direction (measured) and secondary direction (measured or assumed). Furthermore, a minimum magnitude of the secondary magnetization can be calculated with knowledge only of the non-antipodal angle. Applied to three published data sets (sandstone, limestone and diorite intrusion) with non-antipodal angles of 11¿, 28¿ and 11¿ respectively; a secondary component is calculated at 25%, 28% and 16% of the characteristic magnetization remaining after laboratory cleaning. Near surface alteration (weathering) appears to be the source of secondary magnetization in two of these cases. A directionally consistent, biasing effect of a few degrees is made on the mean direction as compared to the conventional calculation of averaging the non-antipodal directions. ¿ American Geophysical Union 1996