It is shown that the observations of occultations of radio sources by the Moon permits the measurement of source positions to an accuracy of the order of 1″. Information is simultaneously obtained on source diameters down to a limit of 1″. The effective beam width of the system on metre wave-lengths is of the order 1/500 sq. degree, and the results are therefore free from the effects of confusion out to distances exceeding those reached in any existing survey. In addition the measurements are not affected by refraction in the Earth's ionosphere or troposphere. The method is illustrated by an analysis of the results obtained from two occultations of the radio source 3C212. The position of this source is derived to an accuracy of 3″. It is shown to be asymmetrical, the diameters along the major and minor axes being 15″ and 7″ respectively. It is suggested that because of its high resolution the method may prove a powerful tool for the investigation of the number/intensity relationship of the discrete sources. It is also pointed out that by carrying out the observations at two frequencies, one above and one below 100 Mc/s, it should be possible to obtain valuable information on a possible lunar ionosphere and perhaps also on other ionized regions in the interplanetary, and possibly interstellar, medium.