The Fourier inversion of all the delay/rate referenced visibilities of Algol was used to form a 'dirty' map which has dramatically improved VLBI array sensitivity. The Algol system, in a very low state of activity with a total flux density of only 3 mJy, was observed alternatively with the reference source 0309 + 411, about 1 deg away, throughout the 7 hr VLBI experiment. By combining all the individual VLBI observations, the resulting coherent integration time for Algol is 4.2 hr and the corresponding SNR is 12. Internal consistency checks and an analysis of possible systematic astrometric errors indicate that the accuracy of the relative VLBI position of Algol is + or - 0.0005 arcsec in both coordinates and that unknown systematic effects are presently limiting this astrometric measurement.