A method for producing tubular knitted articles on a circular knitting machine comprising a needle cylinder with a circular needle bed; wherein the method comprises the following steps: knitting a tubular knitted article starting from an edge and ending with an open toe; arranging coaxially to the needle cylinder a pick-up member, provided with a plurality of pick-up hooks arranged according to a circular ring about an axis of the pick-up member, the circular ring being divided into two circular half-rings (310a, 310b) of pick-up hooks overturnable one onto the other, wherein each pick-up hook comprises: a shank movably constrained to the pick-up member, having a longitudinal axis and ending with a hook portion; and a latch portion having a stem, slidingly constrained to the shank of the hook portion along the longitudinal axis of the shank, and a head configured to co-act with the hook portion; wherein each latch portion is constrained to the shank of the hook portion of the respective pick-up hook, such that each latch portion participates integrally with the movement in radial direction of the hook portion toward and away from the axis of the pick-up member, and each latch portion is movable with respect to the respective hook portion with a movement substantially parallel to the longitudinal axis of the shank of the pick-up hook, so as to be able to move, alternatively, to an open position and a closed position; arranging each pick-up hook in a first position, spaced from the tubular knitted article, wherein in said first position the head of the latch portion holds the hook portion open; pivoting each pick-up hook, integrally with the latch portion, from the first position toward the tubular knitted article to a second position, in which the hook portion of each pick-up hook engages the tubular knitted article and sliding the stem of each latch portion of each pick-up hook along the longitudinal axis of the shank until closing the hook portion, thus preventing the tubular knitted article from being released from the pick-up hooks; removing the tubular knitted article from the needle cylinder by means of said pick-up member and said pick-up hooks engaged to the tubular knitted article; overturning the two circular half-rings (310a, 310b) of the pick-up hooks one onto the other, thus superimposing the two opposite edges of the open toe of the tubular knitted article on each other; joining the two opposite edges to each other forming a closed toe; unloading the tubular knitted article with the closed toe. knitting a tubular knitted article starting from an edge and ending with an open toe; arranging coaxially to the needle cylinder a pick-up member, provided with a plurality of pick-up hooks arranged according to a circular ring about an axis of the pick-up member, the circular ring being divided into two circular half-rings (310a, 310b) of pick-up hooks overturnable one onto the other, wherein each pick-up hook comprises: a shank movably constrained to the pick-up member, having a longitudinal axis and ending with a hook portion; and a latch portion having a stem, slidingly constrained to the shank of the hook portion along the longitudinal axis of the shank, and a head configured to co-act with the hook portion; wherein each latch portion is constrained to the shank of the hook portion of the respective pick-up hook, such that each latch portion participates integrally with the movement in radial direction of the hook portion toward and away from the axis of the pick-up member, and each latch portion is movable with respect to the respective hook portion with a movement substantially parallel to the longitudinal axis of the shank of the pick-up hook, so as to be able to move, alternatively, to an open position and a closed position; arranging each pick-up hook in a first position, spaced from the tubular knitted article, wherein in said first position the head of the latch portion holds the hook portion open; pivoting each pick-up hook, integrally with the latch portion, from the first position toward the tubular knitted article to a second position, in which the hook portion of each pick-up hook engages the tubular knitted article and sliding the stem of each latch portion of each pick-up hook along the longitudinal axis of the shank until closing the hook portion, thus preventing the tubular knitted article from being released from the pick-up hooks; removing the tubular knitted article from the needle cylinder by means of said pick-up member and said pick-up hooks engaged to the tubular knitted article; overturning the two circular half-rings (310a, 310b) of the pick-up hooks one onto the other, thus superimposing the two opposite edges of the open toe of the tubular knitted article on each other; joining the two opposite edges to each other forming a closed toe; unloading the tubular knitted article with the closed toe.