The MX algorithm, due to Schwab (1984), is a variant of the CLARK algorithm in which the clean components are removed from the table at each major cycle. This is the most precise way of removing the found clean components because it avoids aliasing of the dirty sidelobes. A direct consequence is that this method enable to clean the largest region of the dirty map. However, this is a relatively slow algorithm because the imaging step must be redone at each major cycle.