A residual ghost artefact in echo-planar imaging (EPI) remains after the standard correction procedure based on a 1-dimensional phase-modulation of the spectra of even or odd echoes. A better reduction of this artefact is demonstrated using a 2-dimensional phase correction. The phase correction map is measured inside the ghost-free region of the image, preferably in a reference scan with an increased field of view, as the phase difference between complex images reconstructed separately from even and odd echoes. An extrapolated map consisting of spatial components up to the second order (constant, x, y, xy and x2-y2) is then found by a fit to the measured values. This map is used to correct the phase of even- and odd-reconstructed images before adding them. This procedure may cause some spatially dependent loss of signal, but if the level of the residual artefact is less than 20% of the image intensity, such losses are negligible.