The invention refers to a method and apparatus for joining the edges of a tubular knitted article, such as a stocking, upon the completion of the latter on a circular machine; the apparatus comprises a movable carrier able to be associated with a knitting head of a circular machine, and the said carrier supports means for the removal of stitches of the last knitted rank, in which the means operate the removal of one semi-rank, that is, of half the stitches of said last knitted rank, and the means operate the removal of the other semi-rank; the movable carrier being provided with driving means and transfer means able to move the stitches of one semi-rank onto the means which remove the other semi-rank.