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Despite the wealth of studies on seasonal movements of birds between southern nonbreeding locations and High Arctic breeding locations, the key mechanisms of navigation during these migrations remain elusive. A flight along the shortest possible route between pairs of points on a sphere (‘orthodrome’) requires a bird to be able to assess its current location in relation to its migration goal and to make continuous adjustment of heading to reach that goal. Alternatively, birds may navigate along a vector with a fixed orientation (‘loxodrome’) based on magnetic and/or celestial compass mechanisms. Compass navigation is considered especially challenging for summer migrations in Polar regions, as continuous daylight and complexity in the geomagnetic field may complicate the use of both celestial and magnetic compasses here. We examine the possible use of orientation mechanisms during migratory flights across the Greenland Icecap. Using a novel 2 g solar‐powered satellite transmitter, we documented the flight paths travelled by a female red knot Calidris canutus islandica during two northward and two southward migrations. The geometry of the paths suggests that red knots can migrate across the Greenland Icecap along the shortest‐, orthodrome‐like, path instead of the previously suggested loxodrome path. This particular bird's ability to return to locations visited in a previous year, together with its sudden course changes (which would be appropriate responses to ambient wind fields), suggest a map sense that enables red knots to determine location, so that they can tailor their route depending on local conditions.