In order to remove the effect of the diurnal fluctuation of the magnetic field from magnetic measurements recorded at sea, we propose a new method: trigonometric kriging. This method is a particular case of the classical kriging method, but in this case we estimate locally a drift function of the form D(td)=Ai cos (ωti)+Bi sin (ωti) or a truncated Fourier series, using a kriging neighborhood both in time and space. This method does not require any crossing point, which is a major advantage over previously published methods. After presenting the theoretical basis, we show how to put it into practice, i.e., how to choose, both in space and time, the set of points used for the estimation (kriging neighborhood) and how to determine experimentally the model for the generalized covariance which was used in the estimation. Trigonometric kriging has some interesting properties, such as to be exact at track crossings (if any), to allow an only ''almost'' periodic drift to be estimated, and finally to make possible filtering and gridding in one operation. Trigonometric kriging has been applied successfully to several sets of geomagnetic data recorded at sea near the equator, and we show two actual examples in Peru and in Indonesia. ¿ American Geophysical Union 1990