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How the first-order structure of the magnetic field changed through geological time is one of the most long-living and hotly debated questions in geomagnetism. For the last 5 Ma, the geomagnetic field is found to be essentially dipolar with about 5 per cent quadrupole term and, possibly, still smaller octupole term. Proving this became possible after accumulation of a large set of globally distributed reliable palaeomagnetic data and their analysis in the coordinates tied to the rotation axis. For older times, the data are less reliable, scarce and unevenly distributed, while tectonic motions destroyed the global coordinates. In this paper, a method to determine the geomagnetic field structure for a single plate is discussed. It is suggested that the coordinate system for analysis can be derived from great circles, each being drawn through a sampling point and the corresponding palaeomagnetic pole (SP-circle). Such circles are to intersect at a true (i.e. pure dipole) pole that is largely purified from the contributions of non-dipole zonal terms and inclination shallowing. The scrutiny of late Permian (270–250 Ma) palaeomagnetic poles from Northern Eurasia revealed two distinct groups: one includes several poles from a limited area in South France (SF), and the other consists of tightly clustered nine poles from locations spread over a large part of Eurasia. Tentatively, the former group can be explained by either rotation of SF with respect to main Eurasia, or less likely, remagnetization in Early Triassic time; irrespectively, these poles cannot be used for calculation of the true dipole pole nor for computation of the apparent polar wander path of Eurasia. The poles from the main part of Eurasia were used to find the position of the true dipole pole of this plate and for analysis of the field. The minimum of residual dispersion of the observed data is found for the quadrupole and octupole terms of less than 10 per cent when each term is varied separately. When both terms are varied together, the best fit is observed for the quadrupole and octupole terms of −4 and 12 per cent, respectively. Our analysis shows that the position of the true dipole pole is robust, while the estimates of non-dipole terms are not. We argue that these estimates should be regarded as the upper limits on the non-dipole contributions to the Late Permian geomagnetic field; at the same time, we are pretty sure that octupole term of 20 per cent or more are not permitted by the data. [ABSTRACT FROM AUTHOR]