The first image of the full solar corona in the Fe XI 789.2 nm spectral line, acquired during the total solar eclipse of 29 March 2006, with a sequence of 7, 2 and 0.5 second exposures, revealed a surprisingly extended emission out to at least 2R. Enhancements in the Fe XI intensity, with no corresponding enhancements in white light, appeared in different parts of the corona at heights ranging from 1.2 to 1.5R, indicative of an increase of the local Fe10+ density in comparison to the electron density. The extension of the emission is attributed to the dominance of resonant excitation compared to collisional excitation in the formation of the line, a dominance that occurs closer to the solar limb than for the more frequently observed lines of Fe X 637.4 nm and Fe XIV 530.3 nm. The localized enhancements of Fe10+ density can be accounted for by the decoupling of ions and protons there, and hence a localized build-up of ions, as a consequence of insufficient energy input to the ions. The most striking example of enhanced Fe XI intensity occurs above a system of prominences on the south-western limb. These observations are indicative of the existence of sheets of high-density plasma forming from within, or above, prominences, where the heating rate is low. Observations of the Fe XI 789.2 nm emission line, combined with observations in white light proves gives an useful new diagnostic tool for the study of the coronal plasma. Such observations are suitable for existing or future coronagraphs.