A method and apparatus in a drying section of a paper making machine wherein a so-called single-wire draw is applied and wherein blow boxes (20) are used, which are intended to prevent phenomena that disturb the mutual support contact between the web (W) and the drying wire (12). The blow boxes (20) extend across the entire width of the web (W), and they communicate with members (17, 18, 21, 22) that supply blow air, and they are provided with at least two nozzle slots (13, 14) transverse to the running and longitudinal direction of the web (W) as well as with a carrier face (16) between said nozzle slots. Negative pressure is produced in the space (A-) defined by the carrier face (16) and the drying wire (12) by means of the ejection and prevention effects of the air jets (F.sub.1, F.sub.2) blown through the nozzle slots (13,14). In order to speed the threading of the web (W), in the blow boxes (20) the blow sections (24.sub.k+1. . . 24.sub.N ) that remain outside the transverse area (A) of the leader band (R) are closed. The blowing, which has thereby been intensified, is applied through both of the opposite nozzles (13, 14) of the blow boxes (20) in connection with the threading only within the area (A) comprising the width (L.sub.R) of the leader band (R).