A papermaker's fabric is made by spirally winding a woven fabric strip. The fabric strip has first and second lateral edges, along which are a first and second lip, respectively. Each lip has at least one lengthwise yarn woven with crosswise yarns. Adjacent to and inward of the first and second lips on the fabric strip are a first and second gap, respectively, which lack lengthwise yarns but whose crosswise yarns join the lips to the body of the fabric strip. When spirally winding the fabric strip, the first lip is disposed within the second gap, and the second lip is disposed within the first gap, of adjacent turns to form a spirally continuous seam which is closed by attaching adjacent turns to one another.