Alternate-twist plied yarns, wherein a secondary strand for providing a special effect is plied with at least two alternately, false-twisted primary strands, are made by converging the secondary strand with the primary strands downstream of the point at which the primary strands are converged. The nodes at the twist reversal points for the secondary strand are displaced with respect to nodes of the primary strands. Improved effectiveness from the secondary strand in the plied yarn, such as better antistatic performance, can be realized. Where a node of a secondary strand overlaps a node of the primary strands, whether or not the node centers are displaced, a preferred configuration is one wherein the secondary strand forms a node by wrapping around only one of the primary strands in a portion of the primary node.