A method for a sawchain to be used for a sawing arrangement for a forestry harvester in order to prevent the whip-like movement of a sawchain that breaks during sawing, whereby the method comprises the steps: - providing a sawchain comprising a series of links in the form of central driving links and side links (3, 4 and 5) connected in a manner that allows pivoting with the forward and rear parts of the central driving links by means of axes forming pivot points and said axes being located at a distance from each other in the longitudinal direction of the chain, wherein the side links comprise cutting links (3 and 4), and the saw being provided with a means of limiting pivoting that allows a forwardly located link (3, 4, 5, 2) of the sawchain to pivot in a first direction relative to the subsequent link (3, 4, 5, 2) while limiting the ability of the forwardly located link to pivot in an opposite second direction relative to the subsequent link, wherein the means of limiting pivoting is arranged in a region between the pivot points (16, 16) of two neighbouring links (3, 4, 5, 2), wherein the means of limiting pivoting limits pivoting through interaction between opposite edge parts (3a, 4a, 5a, 2a) of the neighbouring links (3, 4, 5, 2), wherein the means of limiting pivoting comprises a member that protrudes in a sideways direction from a driving link and which protruding member occupies a part of the space between the opposite edge parts (3a, 4a, 5a) of the neighbouring side links (3, 4, 5) and forms a stop for the opposite edge parts of the neighbouring side links, wherein the protruding member is located completely above, in said opposite second direction, a central line through the axes of the central driving link, and wherein the protruding member protrudes sideways from the the driving link in one direction such that it is located in a region between two of the opposite edge parts (3a, 4a, 5a) of the neighbouring side links (3, 4, 5), thereby limiting the ability of said forwardly located link to pivot around the axis in the opposite second direction relative to said subsequent link, - driving the sawchain around a guide bar with the aid of a driving wheel that is located at one end of the guide bar, - sawing of a tree trunk is carried out through the guide bar being turned around an axis of rotation. - providing a sawchain comprising a series of links in the form of central driving links and side links (3, 4 and 5) connected in a manner that allows pivoting with the forward and rear parts of the central driving links by means of axes forming pivot points and said axes being located at a distance from each other in the longitudinal direction of the chain, wherein the side links comprise cutting links (3 and 4), and the saw being provided with a means of limiting pivoting that allows a forwardly located link (3, 4, 5, 2) of the sawchain to pivot in a first direction relative to the subsequent link (3, 4, 5, 2) while limiting the ability of the forwardly located link to pivot in an opposite second direction relative to the subsequent link, wherein the means of limiting pivoting is arranged in a region between the pivot points (16, 16) of two neighbouring links (3, 4, 5, 2), wherein the means of limiting pivoting limits pivoting through interaction between opposite edge parts (3a, 4a, 5a, 2a) of the neighbouring links (3, 4, 5, 2), wherein the means of limiting pivoting comprises a member that protrudes in a sideways direction from a driving link and which protruding member occupies a part of the space between the opposite edge parts (3a, 4a, 5a) of the neighbouring side links (3, 4, 5) and forms a stop for the opposite edge parts of the neighbouring side links, wherein the protruding member is located completely above, in said opposite second direction, a central line through the axes of the central driving link, and wherein the protruding member protrudes sideways from the the driving link in one direction such that it is located in a region between two of the opposite edge parts (3a, 4a, 5a) of the neighbouring side links (3, 4, 5), thereby limiting the ability of said forwardly located link to pivot around the axis in the opposite second direction relative to said subsequent link, - driving the sawchain around a guide bar with the aid of a driving wheel that is located at one end of the guide bar, - sawing of a tree trunk is carried out through the guide bar being turned around an axis of rotation.