Abstract: The present invention relates to a process for covering an elastane yarn stretched by three to five times, with a covering yarn, characterised in that it consists:in a first phase, in covering the drawn elastane yarn with the covering yarn with a twist of the order of one third the usual twist of single-covering, and in receiving this covered yarn on a bobbin,then, in a second phase, in taking up this bobbin of covered yarn on a twisting member to communicate thereto an additional twist until a twist which is equal to the usual twist of single-covering is obtained on this yarn.