forming section of a paper making machine includes a double layer or multi layer fabric of interwoven longitudinal and transverse threads and additional transverse threads floating on the paper supporting side the additional transverse threads are interwoven in a plane disposed below the plane formed by the transverse threads of the paper supporting side the additional transverse threads preferably have a smaller diameter than the ordinary transverse threads application_number US 30989389 A description fig1 shows in cross section a first embodiment of the present invention comprising a double layer eight harness fabric double layer in this context means a fabric containing two layers of transverse threads interwoven with a single system of longitudinal threads the top side or paper side of the fabric is formed by mutually interwoven longitudinal threads 1 and upper transverse threads 2 to each one of the upper transverse threads 2 a lower transverse thread 5 is coordinated so that the transverse threads are arranged in pairs the longitudinal threads 1 are also interwoven with the lower transverse threads 5 the lower transverse threads 5 have very long downwardly projecting floats forming the running side of the papermachine fabric since the lower transverse threads 5 are especially exposed to wear they suitably have greater diameter than the upper transverse threads 2 and partially consist of especially wear resistant material e g polyamide and polyester in turn since the longitudinal threads 1 are interwoven with the upper transverse threads 2 and with the lower transverse threads 5 they extend partially on the paper side and partially on the running side of the fabric between the sites where the longitudinal threads 1 are interwoven with the upper and lower transverse threads 2 and 5 they also interweave with.