In contrast to our detailed knowledge of the directional behaviour of the Earth's magnetic field during geological and historical times(1,2), data constraining the past intensity of the field remain relatively scarce. This is mainly due to the difficulty in obtaining reliable palaeointensity measurements, a problem that is intrinsic to the geological materials which record the Earth's magnetic field. Although the palaeointensity database has grown modestly over recent years(3-5), these data are restricted to a few geographical locations and more than one-third of the data record the field over only the past 5 Myr-the most recent database(5) covering the time interval from 5 to 160 Myr contains only about 100 palaeointensity measurements. Here we present 21 new data points from the interval 5-160 Myr obtained from submarine basalt glasses collected from locations throughout the world's oceans. Whereas previous estimates for the average dipole moment were comparable to that of the Earth's present field(6), the new data suggest an average dipole moment of (4.2 +/- 2.3) x 10(22) A m(2), or approximately half the present magnetic-field intensity. This lower average value should provide an important constraint for future efforts to model the convective processes in the Earth's core which have been responsible for generating the magnetic field.