Traditional models of the supercontinent cycle predict that the next supercontinent--'Amasia'--will form either where Pangaea rifted (the 'introversion' model) or on the opposite side of the world (the 'extroversion' models). Here, by contrast, we develop an 'orthoversion' model whereby a succeeding supercontinent forms 90° away, within the great circle of subduction encircling its relict predecessor. A supercontinent aggregates over a mantle downwelling but then influences global-scale mantle convection to create an upwelling under the landmass. We calculate the minimum moment of inertia about which oscillatory true polar wander occurs owing to the prolate shape of the non-hydrostatic Earth. By fitting great circles to each supercontinent's true polar wander legacy, we determine that the arc distances between successive supercontinent centres (the axes of the respective minimum moments of inertia) are 88° for Nuna to Rodinia and 87° for Rodinia to Pangaea--as predicted by the orthoversion model. Supercontinent centres can be located back into Precambrian time, providing fixed points for the calculation of absolute palaeolongitude over billion-year timescales. Palaeogeographic reconstructions additionally constrained in palaeolongitude will provide increasingly accurate estimates of ancient plate motions and palaeobiogeographic affinities.