The current invention concerns an improved system and method for the manufacturing of alternating S/Z cabled yarn 16) or connected alternating S/Z twist plied yarns, in which tension decrease or increase is avoided by variable longitudinal contraction when twist plying or overtwisting yarns. This longitudinal contraction Is very difficult to predict and leads to tension in the yarns, which can affect the quality. This tension can also be reproduced in the installations. This invention tries to improve this by providing a tension compensator (24) that (partially) compensates the tensions and forces between different, subsequent forces for processing yarns.