A method for the production of portions of manufacture by means of a circular knitting machine with a needle cylinder that can be actuated with an alternating rotary motion about its own axis, wherein said needle cylinder has, on its lateral surface, a plurality of axial slots, in each of which a needle is accommodated, a drop or feed being arranged around said needle cylinder and at least one yarn being dispensed thereat which can be engaged by the needles in order to form knitting, means being provided for the actuation of the needles along the corresponding axial slot in order to grip the yarn at said drop or feed and form loops of knitting, selection devices (191, 192) being provided for selecting the needles to be moved to knit at said at least one feed, said selection devices (191, 192) comprising a first selection device and a second selection device, which are arranged on mutually opposite sides with respect to said feed, said selection devices (191, 192) being adapted to select the needles downstream of said feed depending on the direction of rotation (201 or 202) of the needle cylinder about its own axis, characterized in that it comprises the following steps: - identifying a group of contiguous needles in the needle cylinder; - dividing said group of needles into two contiguous needle subgroups (13-72 and 73-132), respectively a first needle subgroup and a second needle subgroup; - moving to knit at said feed a needle subgroup (13-72 or 73-132) of said two needle subgroups (13-72, 73-132) during the rotation of the needle cylinder in one direction (201 or 202) and in the subsequent rotation in the opposite direction (202 or 201) to form two partial rows of knitting (301, 302 or 303, 304) in succession; - moving to knit at said feed the other needle subgroup (73-132 or 13-72) of said two needle subgroups (13-72, 73-132) during the rotation of the needle cylinder in one direction of rotation (202 or 201) and in the subsequent rotation in the opposite direction (201 or 202) to form two partial rows of knitting (303, 304 or 301, 302) in succession; - proceeding in this manner by alternating, every two partial rows of knitting (301, 302 or 303, 304), the needle subgroup (13-72 or 73-132) that is moved to knit at said feed for a preset number of partial rows of knitting (301, 302, 303, 304); at least one needle (72, 73) of a needle subgroup (13-72 or 73-132) of said needle subgroups (13-72, 73-132), located proximate to the other needle subgroup (73-132 or 13-72), being moved to knit in the forming of at least one of the two partial rows of knitting (301, 302 or 303, 304) formed in each instance by the other needle subgroup (13-72 or 73-132) for the interconnection of the partial rows of knitting (301, 302 or 303, 304) formed by a needle subgroup (13-72 or 73-132) with the partial rows of knitting (303, 304 or 301, 302) formed by the other needle subgroup (73-132 or 13-72). - identifying a group of contiguous needles in the needle cylinder; - dividing said group of needles into two contiguous needle subgroups (13-72 and 73-132), respectively a first needle subgroup and a second needle subgroup; - moving to knit at said feed a needle subgroup (13-72 or 73-132) of said two needle subgroups (13-72, 73-132) during the rotation of the needle cylinder in one direction (201 or 202) and in the subsequent rotation in the opposite direction (202 or 201) to form two partial rows of knitting (301, 302 or 303, 304) in succession; - moving to knit at said feed the other needle subgroup (73-132 or 13-72) of said two needle subgroups (13-72, 73-132) during the rotation of the needle cylinder in one direction of rotation (202 or 201) and in the subsequent rotation in the opposite direction (201 or 202) to form two partial rows of knitting (303, 304 or 301, 302) in succession; - proceeding in this manner by alternating, every two partial rows of knitting (301, 302 or 303, 304), the needle subgroup (13-72 or 73-132) that is moved to knit at said feed for a preset number of partial rows of knitting (301, 302, 303, 304);