Recent studies have shown that magnetic fields in the solar corona are strong enough to significantly mix the two 3p(4)3d (4)D(5/2,7/2)levels in Cl-like Fex. This mixing gives rise to a magnetically induced transition (MIT) component in the bright Fex257.3 angstrom line, commonly observed by current instrumentation, that can be used for coronal magnetic field diagnostics. This line, commonly observed by the still operational EIS spectrometer on board the Hinode satellite since 2007, opens a new window into the coronal magnetic field. However, the strength of this MIT transition depends on the square of the energy difference Delta E of the two 4D(5/2,7/2) levels, so that an accurate determination of Delta E is of critical importance to accurately measure coronal magnetic field strengths. In the present work we present a new measurement of Delta Eobtained determining the separation of the two component of the Fexdoublet close to 1603.3 A from deep-exposure spectra of a quiescent streamer at the solar limb taken with the SUMER instrument on board SoHO. Our measurement of Delta E = 2.29 0.50 cm(-1) agrees with, and improves upon, an earlier measurements by Judge et al. by decreasing its uncertainty from 80% to approximately 20%, improving the attainable accuracy of magnetic field strength measurements obtainable with the Fex257.26 angstrom line.